# Outbreak detection algorithms based on generalized linear model a review with new practical

# Outbreak detection algorithms based on generalized linear model: a review with new practical examples

Surveillance of the population's health status is the most important function in the health system, ensuring the monitoring, early detection and prevention of infectious diseases. In recent years, flash detection algorithms have become very important in various surveillance systems, especially in the light of the pandemic Covid-19. We consider these algorithms from both theoretical and practical perspectives. The theoretical side includes the development and implementation of new statistical methods that arouse interest among statisticians. On the other hand, the practical side includes the development of flash detection systems and the use of different techniques for monitoring symptomatic symptoms, which have attracted the attention of epidemiologists and health care managers. During the last three decades, a great deal of effort has been made in the field of epidemiology, resulting in valuable publications presenting new statistical methods and comparing their effectiveness. The generalized linear model (OLM) family has undergone several changes compared to other statistical methods and models. The aim of this study is to present and explain a method based on GLM, ensuring its consistent comparison. First, we give a historical overview of flash detection algorithms based on the GLM family.

## Background

Involvement, regular collection, analysis of data for social health care, aimed at social health care, aimed at reducing the incidence and mortality rate through measures related to well treatments and strengthening social welfare. The process of interpretation and dissemination is called infectious disease [1]. One of the guidance goals for infectious diseases is to discover the outbreak in a timely manner, and this can actually conduct a survey almost immediately and realize countermeasures. In recent years, the infectious disease system for achieving this goal has been significantly increased. Behind this is the growing concern about the occurrence of a larg e-scale biology attack, and the increasing awareness of the general public about the resulting and recurring emerging infectious diseases. These benefits were the introduction of syndrome-epidemiological systems, the construction of a database, and the construction of an automatic burst system that handles many wave data. [2] The effectiveness of flare wound detection due to syndrome observation and automatic system depends on the detection of statistical abnormalities. If the number of suspected cases recorded by the epidemic system increases significantly higher than the expected value or the worthy value, the number of cases is significantly higher than the expected number or value. It means that it has increased. < SPAN> Invisible and regular collection of data aimed at social healthcare aimed at reducing the incidence and mortality rate through measures related to well treatments and strengthening social welfare. The process of analysis, interpretation, and dissemination is called infectious disease [1]. One of the guidance goals for infectious diseases is to discover the outbreak in a timely manner, and this can actually conduct a survey almost immediately and realize countermeasures. In recent years, the infectious disease system for achieving this goal has been significantly increased. Behind this is the growing concern about the occurrence of a larg e-scale biology attack, and the increasing awareness of the general public about the resulting and recurring emerging infectious diseases. These benefits were the introduction of syndrome-epidemiological systems, the construction of a database, and the construction of an automatic burst system that handles many wave data. [2] The effectiveness of flare wound detection due to syndrome observation and automatic system depends on the detection of statistical abnormalities. If the number of suspected cases recorded by the epidemic system increases significantly higher than the expected value or worse value, the number of cases is significantly higher than the expected number of cases or the values. It means that it has increased. Involvement, regular collection, analysis of data for social health care, aimed at social health care, aimed at reducing the incidence and mortality rate through measures related to well treatments and strengthening social welfare. The process of interpretation and dissemination is called infectious disease [1]. One of the guidance goals for infectious diseases is to discover the outbreak in a timely manner, and this can actually conduct a survey almost immediately and realize countermeasures. In recent years, the infectious disease system for achieving this goal has been significantly increased. Behind this is the growing concern about the occurrence of a larg e-scale biology attack, and the increasing awareness of the general public about the resulting and recurring emerging infectious diseases. These benefits have led to the introduction of syndrome-epidemiological systems, the construction of a database, and the construction of an automatic burst system that processes many wave data. [2] The effectiveness of flare wound detection due to syndrome observation and automatic system depends on the detection of statistical abnormalities. If the number of suspected cases recorded by the epidemic system increases significantly higher than the expected value or the worthy value, the number of cases is significantly higher than the expected number or value. It means that it has increased.

The development of statistical methods has been strengthened due to the desire to improve the algorithm that detects flashing dark points due to early detection of illness. Various categories are provided in the detection method. For example, UNKEL, et al. (2012), how to find these algorithms (time series, statistical process control, GLM family, etc.) and thresholds (parametric methods, sem i-imetric methods, no n-parametric methods, no n-parametric methods, no n-surveyed methods. Classified based on the method, etc.). Some papers classify outbreak detection algorithms based on more common different systems. Buckeride et al. (2003) presented a spatial spatial analysis structure, and FeverJon and Berezowski (2018) classify the conceptual framework of time algorithm in the syndrome observation system [4, 5]. The use of different algorithms for flash detection and the interconnection of these methods was conducted in several papers based on simulation data and actual data. Among them, Bédubourget. (2017) [6]. < SPAN> The development of statistical methods has been strengthened due to the desire to improve the algorithm that detects flashing dark points for early detection of the disease. Various categories are provided in the detection method. For example, UNKEL, et al. (2012), how to find these algorithms (time series, statistical process control, GLM family, etc.) and thresholds (parametric methods, sem i-imetric methods, no n-parametric methods, no n-parametric methods, no n-surveyed methods. Classified based on the method, etc.). Some papers classify outbreak detection algorithms based on more common different systems. Buckeride et al. (2003) presented a spatial spatial analysis structure, and FeverJon and Berezowski (2018) classify the conceptual framework of time algorithm in the syndrome observation system [4, 5]. The use of different algorithms for flash detection and the interconnection of these methods was conducted in several papers based on simulation data and actual data. Among them, Bédubourget. (2017) [6]. For early detection of the disease, the development of statistical methods has been strengthened by the desire to improve the algorithm that detects flashing darkness. Various categories are provided in the detection method. For example, UNKEL, et al. (2012), how to find these algorithms (time series, statistical process control, GLM family, etc.) and thresholds (parametric methods, sem i-imetric methods, no n-parametric methods, no n-parametric methods, no n-surveyed methods. Classified based on the method, etc.). Some papers classify outbreak detection algorithms based on more common different systems. Buckeride et al. (2003) presented a spatial spatial analysis structure, and FeverJon and Berezowski (2018) classify the conceptual framework of time algorithm in the syndrome observation system [4, 5]. The use of different algorithms for flash detection and the interconnection of these methods was conducted in several papers based on simulation data and actual data. Among them, already bédubourget. (2017) [6].

In the comments, the method of flash detection based on GLM generation is being considered. The value of considering the genus GLM is explained in the following path. The generalized line model can simulate the relationship between variable resonance (for example, the number of cases of illness) and one or more variables-investigators (age, gender, location, time, etc.). It is a class. The GLM has expanded the linear regression model to handle the abnormal distribution of variable resonance, and this binary, count, and continuous data have unstable diversification. GLM realizes this method to show a communication function that connects the expected variable resonance to the predictive variable linear configuration, for example, to shows the contrary communication functions for the number of data. The choice of communication functions depends on the data of resonance variables and the research issues under consideration. The GLM also supports the distributed function to simulate the variable resonance variable that can be set for all kinds of data. In this way, GLM models a flexible and reliable database to model the incidence data and identifies what is likely to occur. The method of ignition detection based on the GLM is examined in Eigendo < SPAN> comments for flash detection based on GLM generation. The value of considering the genus GLM is explained in the following path. The generalized line model can simulate the relationship between variable resonance (for example, the number of cases of illness) and one or more variables-investigators (age, gender, location, time, etc.). It is a class. The GLM has expanded the linear regression model to handle the abnormal distribution of variable resonance, and this binary, count, and continuous data have unstable diversification. GLM realizes this method to show a communication function that connects the expected variable resonance to the predictive variable linear configuration, for example, to shows the contrary communication functions for the number of data. The choice of communication functions depends on the data of resonance variables and the research issues under consideration. The GLM also supports the distributed function to simulate the variable resonance variable that can be set for all kinds of data. In this way, GLM models a flexible and reliable database to model the incidence data and identifies what is likely to occur. The method of ignition detection based on the GLM is examining the method of flash detection based on the GLM generation in Eigendo comments. The value of considering the genus GLM is explained in the following path. The generalized line model can simulate the relationship between variable resonance (for example, the number of cases of illness) and one or more variables-investigators (age, gender, location, time, etc.). It is a class. The GLM has expanded the linear regression model to handle the abnormal distribution of variable resonance, and this binary, count, and continuous data have unstable diversification. GLM realizes this method to show a communication function that connects the expected variable resonance to the predictive variable linear configuration, for example, to shows the contrary communication functions for the number of data. The choice of communication functions depends on the data of resonance variables and the research issues under consideration. The GLM also supports the distributed function to simulate the variable resonance variable that can be set for all kinds of data. In this way, GLM models a flexible and reliable database to model the incidence data and identifies what is likely to occur. The method of detecting fire based on GLM is Eigendo

These are tracked by the research system and are reported to the Honey organization (in this case, the Ministry of Health). Based on Farington's ideas, for example, how to detect flashes must be quite reliable to overcome low illnesses and high illnesses. Salmonella is considered a good example of these diseases, especially the Typhimurium DT104 shares, which have at least 100 weeks, and the rotaviruses, which have a certain number of weeks of a specific number of weeks. < SPAN> These are tracked by the research system and are reported to the Honey organization (in this case, the Ministry of Health). Based on Farington's ideas, for example, how to detect flashes must be quite reliable to overcome low illnesses and high illnesses. Salmonella is considered a good example of these diseases, especially the Typhimurium DT104 shares, which have at least 100 weeks, and the rotaviruses, which have a certain number of weeks of a specific number of weeks. These are tracked by the research system and are reported to the Honey organization (in this case, the Ministry of Health). Based on Farington's ideas, for example, how to detect flashes must be quite reliable to overcome low illnesses and high illnesses. Salmonella is considered a good example of these diseases, especially the Typhimurium DT104 shares, which have at least 100 weeks, and the rotaviruses, which have a certain number of weeks of a specific number of weeks.

## Main text

### History

As the development of flash detection algorithms progresses, the diversity of algorithms based on the GLM family is increasing. Along with the advantages of GL M-based techniques, the diversity of these methods is another important reason for writing this review. Such diversity is rarely seen in other techniques, and can bring confusion to people who are interested in this field. These slight differences between these methods in statistical theory can sometimes lead to errors in practice. Another reason for choosing a GLM family is that it is popular among public health and epidemiology researchers. The GLM family is often used in various research methodology. Thanks to this, researchers who want to study and use these methods in the field of algorithms that detect epidemiology and illness are more likely to study and use these methods. The generalized method model (GAM) is a sem i-parametric expansion of GLM and is also used in flash detection algorithm. See [11] and [12] for details on this topic. The use of a flash detection algorithm based on GAM gives you a unique advantage. However, since research in this field is not enough, this study focused on the GLM family. Furthermore, as R e-PROGRA < SPAN> flash detection algorithm develops, the diversity of algorithms based on the GLM family is increasing. Along with the advantages of GL M-based techniques, the diversity of these methods is another important reason for writing this review. Such diversity is rarely seen in other techniques, and can bring confusion to people who are interested in this field. These slight differences between these methods in statistical theory can sometimes lead to errors in practice. Another reason for choosing a GLM family is that it is popular among public health and epidemiology researchers. The GLM family is often used in various research methodology. Thanks to this, researchers who want to study and use these methods in the field of algorithms that detect epidemiology and illness are more likely to study and use these methods. The generalized method model (GAM) is a sem i-parametric expansion of GLM and is also used in flash detection algorithm. See [11] and [12] for details on this topic. The use of a flash detection algorithm based on GAM gives you a unique advantage. However, since research in this field is not enough, this study focused on the GLM family. Furthermore, as the development of the R e-PROGRA flash detection algorithm progresses, the diversity of algorithms based on the GLM family is increasing. Along with the advantages of GL M-based techniques, the diversity of these methods is another important reason for writing this review. Such diversity is rarely seen in other techniques, and can cause confusion to people who are interested in this field. These slight differences between these methods in statistical theory can sometimes lead to errors in practice. Another reason for choosing a GLM family is that it is popular among public health and epidemiology researchers. The GLM family is often used in various research methodology. Thanks to this, researchers who want to study and use these methods in the field of algorithms that detect epidemiology and illness are more likely to study and use these methods. The generalized method model (GAM) is a sem i-parametric expansion of GLM and is also used in flash detection algorithm. See [11] and [12] for details on this topic. The use of a flash detection algorithm based on GAM gives you a unique advantage. However, since research in this field is not enough, this study focused on the GLM family. Furthermore, R e-program

The detection algorithm based on the GLM family was introduced under the management diagram [13] of Shewhart (1931). The variable represents the frequency of time T illness in the monitoring system and is a normal distribution ► (n ◄left (nmu ^right) ◄. According to the shewhart (Shewhart) management diagram, at κ ≧ 0. The reasons for this increase are the glu m-based outbreaks, which are generated in the time T. In order to make three important changes, the average and dispersion of the probability variables and the diversion of the shoehart are dynamic. These parameters can be estimated from past input data. In order to estimate pneumonia and influenza weekly mortality data, the

### Original farrington

Here, ∆ (_) is the number of people affected by T weeks/ month, and the signing and cosine section indicate seasonal changes. Costagliola's research conducted in 1991 is based on the Serfling Law, diagnosing influenz a-like syndrome in the survay lance system from 1984 to 1988, and predicts the next no n-epidemic level in the next winter. [14] In this method, the subset of all data must be selected as "training period" first. Next, the data on the past outbreak is excluded from the training period. For example, a value of 15 % of the maximum value can be excluded. Finally, a regression formula based on the surfing method must be applied to predict the expected no n-trendy level. In order to give a warning to the excessive radiation detection algorithm based on this method, the upper limit must be considered by selecting a top percentile of the predictive value. In this method, parameters are estimated using the tw o-square average square root error method [8, 14]. One of the main limits of this technique is how to determine the epidemic period, that is, how much data observed in the past trends should be excluded when applying a model. Another limit is that applying a regression model that assumes a regular error distribution may be inappropriate.

Since many data from the Surveyance system is excessively distributed, Farrington eton (1996) introduces a quas i-poreson regression model and applies to early discovery of outbreaks based on reports from the infection survay lance center (CDSC). did.<\upmu >The average ‡ (average ‡ (average ‡ () is set to the number of bassline diseases of the Survey lance system corresponding to the base line week ‡.<\mathrm<\varphi \mu >And dispersed ___________________________________________________

And. ) Considering the linear time tendency in the frequency of recorded diseases, the regression model is defined as follows:<\mu >Glink (Right) = $ α +$ β_, $k. < SPAN> Here, ∆ (_) is the number of affected people in T week/ month, and the signing and cosine terms represent seasonal changes. Costagliola's research conducted in 1991 is based on the Serfling Law, diagnosing influenz a-like syndrome in the survay lance system from 1984 to 1988, and predicts the next no n-epidemic level in the next winter. [14] In this method, the subset of all data must be selected as "training period" first. Next, the data on the past outbreak is excluded from the training period. For example, a value of 15 % of the maximum value can be excluded. Finally, a regression formula based on the surfing method must be applied to predict the expected no n-trendy level. In order to give a warning to the excessive radiation detection algorithm based on this method, the upper limit must be considered by selecting a top percentile of the predictive value. In this method, parameters are estimated using the tw o-square average square root error method [8, 14]. One of the main limits of this technique is how to determine the epidemic period, that is, how much data observed in the past trends should be excluded when applying a model. Another limit is that applying a regression model that assumes a regular error distribution may be inappropriate.

Since many data from the Surveyance system is excessively distributed, Farrington eton (1996) introduces a quas i-poreson regression model and applies to early discovery of outbreaks based on reports from the infection survay lance center (CDSC). did.

The average ‡ (average ‡ (average ‡ () is set to the number of bassline diseases of the Survey lance system corresponding to the base line week ‡.

And dispersed ___________________________________________________Glink (

Right) = $ α +$ β_, $k. Here, ∆ (_) is the number of people affected by T weeks/ month, and the signing and cosine section indicate seasonal changes. Costagliola's research conducted in 1991 is based on the Serfling Law, diagnosing influenz a-like syndrome in the survay lance system from 1984 to 1988, and predicts the next no n-epidemic level in the next winter. [14] In this method, the subset of all data must be selected as "training period" first. Next, the data on the past outbreak is excluded from the training period. For example, a value of 15 % of the maximum value can be excluded. Finally, a regression formula based on the surfing method must be applied to predict the expected no n-trendy level. In order to give a warning to the excessive radiation detection algorithm based on this method, the upper limit must be considered by selecting a top percentile of the predictive value. In this method, parameters are estimated using the tw o-square average square root error method [8, 14]. One of the main limits of this technique is how to determine the epidemic period, that is, how much data observed in the past trends should be excluded when applying a model. Another limit is that applying a regression model that assumes a regular error distribution may be inappropriate.

Since many data from the Surveyance system is excessively distributed, Farrington eton (1996) introduces a quas i-poreson regression model and applies to early discovery of outbreaks based on reports from the infection survay lance center (CDSC). did.<\mu>The average ‡ (average ‡ (average ‡ () is set to the number of bassline diseases of the Survey lance system corresponding to the base line week ‡.<\mu>_.$$And dispersed ___________________________________________________

- Glink (
- Here, (g) (.) In the communication function of communication, all numbers are obtained using the sem i-body method. The following model assumes that the transmission function connecting the average response variable and the linear combination is a logarithmic. However, the Jackson model is an exception, and the transmission function must be linear (G ∕ Left (X ∕ Right) = X ∕ Right). The week is used as a unit of time. In the infectious disease system, the time measurement on a monthly basis is not recommended because the early detection of a disease case is one of the goals.
- In the case of a porson distribution and a negative tw o-term distribution, the distortion correction using 2/3 applicable is as follows.
- Right) = O (
- Here, ‡ (_ ‡) is 100 ( 1-α) -percentage of normal distribution, A ‡ (TAU) -This.
- Right < Span> Here, (g) (.) In the communication function of communication, all numbers are obtained using the sem i-body law. The following model assumes that the transmission function connecting the average response variable and the linear combination is a logarithmic. However, the Jackson model is an exception, and the transmission function must be linear (G ∕ Left (X ∕ Right) = X ∕ Right). The week is used as a unit of time. In the infectious disease system, the time measurement on a monthly basis is not recommended because the early detection of a disease case is one of the goals.
- In the case of a porson distribution and a negative tw o-term distribution, the distortion correction using 2/3 applicable is as follows.
- Right) = O (
- Here, ‡ (_ ‡) is 100 ( 1-α) -percentage of normal distribution, A ‡ (TAU) -This.

Town = φ PHI + var Left (Hat)

Right here, (g) (.) In the communication function of communication, all numbers are obtained using the sem i-body method. The following model assumes that the transmission function connecting the average response variable and the linear combination is a logarithmic. However, the Jackson model is an exception, and the transmission function must be linear (G ∕ Left (X ∕ Right) = X ∕ Right). The week is used as a unit of time. In the infectious disease system, the time measurement on a monthly basis is not recommended because the early detection of a disease case is one of the goals.

### Farrington flexible

By selecting a linear time variable, a trend was incorporated into the regression model. This coordinated loose linear regression is very sensitive to the r e-distribution, and can also detect a significant increase in the number of lo w-generated diseases, and a significant increase in the number of reports of hig h-generation diseases. According to Farrington (1996) studies, there are some things that I want to skip here easily. Farrington eton (1996) indicates that after creating a graph with average amounts of microorganisms per week, the porassa distribution matches the graph of distributed distributed amount of microbial amounts per week. 。 (1996) showed that the assumption of the poisson distribution was unreasonable when the average value was less than one unit. If the average value is 10 or more, the distribution will be asymptotic to the asymptload. In addition, organisms with low incidence have a very asymmetric distribution. Correction of asymptomaticity by converting data by changing the threshold by changing the threshold in a situation where excessive dispersion can reduce the number of fake.

In the case of a porson distribution and a negative tw o-term distribution, the distortion correction using 2/3 applicable is as follows.

Left (left (For large media, a trust section ((LU) ⓐ) is led by the Taylor class.

Here, ‡ (_ ‡) is 100 ( 1-α) -percentage of normal distribution, A ‡ (TAU) -This.

### Some regression models mentioned in the articles

#### Jackson model

Town = φ PHI + var Left (Hat)

Left (left (3. R e-assembly of the model

### Periodic poisson GLM method

overview<\mu >4. Estimation of excess distribution

{Ruit}

### Poisson regression charts based on generalized likelihood ratio (GLR)

5. Scale model

{Ruit}

6. Rejection of career change when judged not important<\mu >Discard} {Ruit<\mu >7. Repeat all steps<\mu >_=<\mu >{Ruit}.

Left (left (9. Calculation of excess score

$$<\mu >_=<\mu >The presented diagram corresponds to the nine steps described in the research. Rice 1 is designed to be literally suggested by each step, and is carefully designed to secure a comfortable visual support for readers (Figure 1).Farrington's algorithm is sold in the "Observation" package of the R program.

- Data collection and reporting in the plague system have lon g-term changes, so it is not recommended to increase the number of years to include more initial data. An alternative is to use more recent data and add seasonal fluctuations to the formula of the Farrington model. This model estimates the number of affected people in the past week, includes linear trends and 1 0-level annual coefficients, and includes past similar weeks. The corresponding linear logarithmic model is as follows:
- Here
- Mathrm

Here

Here, (j (_) ⊖) is the seasonal coefficient corresponding to the week. Assuming j (j (left) (left) (_ (right))) = 0 ω) and ω (_ = 0 ω), this model, except in the case of very thin data, regardless of statistical significance. The trend is always considered. The effects of past occurrence are reduced using more than 2 and 58 Ansskyba residues. Data collection and reporting in the plague system have lon g-term changes, so it is not recommended to increase the number of years to include more initial data. An alternative is to use more recent data and add seasonal fluctuations to the formula of the Farrington model. This model estimates the number of affected people in the past week, includes linear trends and 1 0-level annual coefficients, and includes past similar weeks. The corresponding linear logarithmic model is as follows:

MathrmMathrm

\ Link (

### Comparing farrington, farrington flexible, jackson, periodic poisson GLM, and GLR algorithms for disease outbreak detection

Right) = β 0+ β 1 dots

+\ dots +label 6 text

- ) +Label 18 (Mathrm) +Label 19 (Mathrm). < SPAN> This model is used for overrunning overrans death. Alignments based on the evaluation of ove r-mortality rate can take into account the suppression of mortality due to epidemic. For example, as in the case of Pandemic COVID-19, various methods such as Farrington Law [16, 17] are proposed to evaluate the over-mortality rate in tight victims. However, one of the leading tasks in implementing this method is that the data size is small, especially for new diseases. Without the required number of data, the accuracy of evaluation and monitoring may be reduced, and the outbreak prediction may be incorrect. The hole was coded into a survay lance package under the title Farrington Flexible. The implementation is considered to be one of the Salmon et al. Farrington Flexible methods used to predict weekly data in public health England, which is an early amber report system (EARS). It is considered to be a normal CDC US system for syndrome observation. Scientists are interested in applying the daily prediction system of plague, as the importance of discovering early outbreaks and the main requirements are to prevent them from being involved in conflicts in the event of a global event. I am.
- Mathrm
- Right) = β 0+ β 1 dots
- + \ dots + text
- Jackson et al. (2007) came up with a GLM model based on the Poisson distribution using three years of initial data and Poasson mistakes. This model provides the effects of the day, the month, and the course of the course, and the influence of magnificent variables. The expected frequency model on the T-day includes the following format:
- \ Link (
- +\ dots +label 6 text
- ) +Label 18 (Mathrm) +Label 19 (Mathrm).
_{1}If you have a population data, the 2nd Logistic model can be built in the same way as the Poisson distribution model. The flexibility of the GLM approach can include more variables, such as random effects [26], based on the opinions of researchers. As mentioned at the beginning, regression models can be conformed to various types of data and can meet specific requirements for given groups and diseases. However, a single regression using a minimum square method alone is not enough to remove the systematic effects of epidemiological data. This is due to the fact that the residual regression by the minimum square method suggests that the residue is independent and the same distribution. In many cases, epidemiological data is contrary to this assumption, and the residue may not be independent or does not support normal distribution. To solve these problems, a more sophisticated regression method is required. These methods can be taken into account the bias and independence of the residue, and needs to remove the systematic effects of data. Therefore, it is important to select an appropriate regression method based on the nature of the data and the issues of research and research [27, 28]._{1}Based on the modeled data of Bédubourg et al. - According to this model, the average value is equal to the prediction value of the T week of T week, and the dispersion is evaluated by the negative binary distribution using a model [6]. We call this method in Table 2 as the "periodic Poisson GLM Law".

Try to follow the parametric distribution of _ _ cdots. 変化点τ について，条件付き密度 ________ (_ | _ ________) は，次のように決定される

### New examples of outbreak detection algorithms based on GLM for surveillance system

Here, c o-diversification is known in time t, time t shows known coexistence, timely c o-diversificatio n-Poasson Functions of ProbiCity Density coordinates (

t & amp; amp; gt; ⌫ and __ (

T & amp; amp; gt; gt). In other words, new data is collected until the researcher notices changes in the presented data. The rule to stop the specimen under conditions other than the observation system is when there is enough evidence of the returnless hypothesis; __________________________________________________________________________________________________________________________________________::::::::::::::

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