A useful distribution for fitting discrete data: revival of the Conway-Maxwell-Poisson distribution

2005 ◽  
Vol 54 (1) ◽  
pp. 127-142 ◽  
Author(s):  
Galit Shmueli ◽  
Thomas P. Minka ◽  
Joseph B. Kadane ◽  
Sharad Borle ◽  
Peter Boatwright
Keyword(s):  
Poisson Distribution ◽  
Discrete Data

scholarly journals A Generalised Exponential-Lindley Mixture of Poisson Distribution

2019 ◽  
Vol 3 ◽  
pp. 11-20
Author(s):  
Binod Kumar Sah ◽  
A. Mishra
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Mixture Distribution ◽  
Discrete Data ◽  
Likelihood Method ◽  
P Value ◽  
Data Set ◽  
Lindley Distribution ◽  
First Four Moments

Background: The exponential and the Lindley (1958) distributions occupy central places among the class of continuous probability distributions and play important roles in statistical theory. A Generalised Exponential-Lindley Distribution (GELD) was given by Mishra and Sah (2015) of which, both the exponential and the Lindley distributions are the particular cases. Mixtures of distributions form an important class of distributions in the domain of probability distributions. A mixture distribution arises when some or all the parameters in a probability function vary according to certain probability law. In this paper, a Generalised Exponential- Lindley Mixture of Poisson Distribution (GELMPD) has been obtained by mixing Poisson distribution with the GELD. Materials and Methods: It is based on the concept of the generalisations of some continuous mixtures of Poisson distribution. Results: The Probability mass of function of generalized exponential-Lindley mixture of Poisson distribution has been obtained by mixing Poisson distribution with GELD. The first four moments about origin of this distribution have been obtained. The estimation of its parameters has been discussed using method of moments and also as maximum likelihood method. This distribution has been fitted to a number of discrete data-sets which are negative binomial in nature and it has been observed that the distribution gives a better fit than the Poisson–Lindley Distribution (PLD) of Sankaran (1970). Conclusion: P-value of the GELMPD is found greater than that in case of PLD. Hence, it is expected to be a better alternative to the PLD of Sankaran for similar type of discrete data-set which is negative binomial in nature.

Analysis of discrete data by Conway–Maxwell Poisson distribution

2014 ◽  
Vol 98 (4) ◽  
pp. 327-343 ◽  
Author(s):  
Ramesh C. Gupta ◽  
S. Z. Sim ◽  
S. H. Ong
Keyword(s):  
Poisson Distribution ◽  
Discrete Data

scholarly journals A Generalised Poisson Mishra Distribution

2018 ◽  
Vol 2 ◽  
pp. 27-36
Author(s):  
Binod Kumar Sah
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial ◽  
Mass Function ◽  
Discrete Data ◽  
P Value ◽  
Probability Mass Function ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
First Moment ◽  
First Four Moments

Background: “Mishra distribution" of B. K. Sah (2015) has been obtained in honor of Professor A. Mishra, Department of Statistics, Patna University, Patna (Sah, 2015). A one parameter Poisson-Mishra distribution (PMD) of B. K. Sah (2017) has been obtained by compounding Poisson distribution with Mishra distribution. It has been found that this distribution gives better fit to all the discrete data sets which are negative binomial in nature used by Sankarn (1970) and others. A generalisation of PMD has been obtained by mixing the generalised Poisson distribution of Consul and Jain (1973) with the Mishra distribution.Materials and Methods: It is based on the concept of the generalisations of some continuous mixtures of Poisson distribution.Results: Probability density function and the first four moments about origin of the proposed distribution have been obtained. The estimation of parameters of this distribution has been discussed by using the first moment about origin and the probability mass function at x = 0 . This distribution has been fitted to a number of discrete data-sets to which earlier Poisson-Lindley distribution (PLD) and PMD have been fitted.Conclusion: P-value of generalised Poisson-Mishra distribution is greater than PLD and PMD. Hence, it provides a better alternative to the PLD of Sankarn and PMD of B. K. Sah.Nepalese Journal of Statistics, Vol. 2, 27-36

Zero-inflated Conway-Maxwell Poisson Distribution to Analyze Discrete Data

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Shin Zhu Sim ◽  
Ramesh C. Gupta ◽  
Seng Huat Ong
Keyword(s):  
Regression Model ◽  
Poisson Distribution ◽  
Likelihood Ratio ◽  
Regression Models ◽  
Discrete Data ◽  
Likelihood Ratio Tests ◽  
Simulation Studies ◽  
Generalized Poisson ◽  
Proposed Model ◽  
Better Than

Abstract In this paper, we study the zero-inflated Conway-Maxwell Poisson (ZICMP) distribution and develop a regression model. Score and likelihood ratio tests are also implemented for testing the inflation/deflation parameter. Simulation studies are carried out to examine the performance of these tests. A data example is presented to illustrate the concepts. In this example, the proposed model is compared to the well-known zero-inflated Poisson (ZIP) and the zero- inflated generalized Poisson (ZIGP) regression models. It is shown that the fit by ZICMP is comparable or better than these models.

scholarly journals On a Generalised Exponential-Lindley Mixture of Generalised Poisson Distribution

2020 ◽  
Vol 4 ◽  
pp. 33-42
Author(s):  
Binod Kumar Sah ◽  
A. Mishra
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial ◽  
Mixture Distribution ◽  
Discrete Data ◽  
P Value ◽  
Data Sets ◽  
Mixing Distribution ◽  
Original Distribution ◽  
Compound Distribution ◽  
First Four Moments

Background: A mixture distribution arises when some or all parameters in a mixing distribution vary according to the nature of original distribution. A generalised exponential-Lindley distribution (GELD) was obtained by Mishra and Sah (2015). In this paper, generalized exponential- Lindley mixture of generalised Poisson distribution (GELMGPD) has been obtained by mixing generalised Poisson distribution (GPD) of Consul and Jain’s (1973) with GELD. In the proposed distribution, GELD is the original distribution and GPD is a mixing distribution. Generalised exponential- Lindley mixture of Poisson distribution (GELMPD) was obtained by Sah and Mishra (2019). It is a particular case of GELMGPD. Materials and Methods: GELMGPD is a compound distribution obtained by using the theoretical concept of some continuous mixtures of generalised Poisson distribution of Consul and Jain (1973). In this mixing process, GELD plays a role of original distribution and GPD is considered as mixing distribution. Results: Probability mass of function (pmf) and the first four moments about origin of the generalised exponential-Lindley mixture of generalised Poisson distribution have been obtained. The method of moments has been discussed to estimate parameters of the GELMGPD. This distribution has been fitted to a number of discrete data-sets which are negative binomial in nature. P-value of this distribution has been compared to the PLD of Sankaran (1970) and GELMPD of Sah and Mishra (2019) for similar type of data-sets. Conclusion: It is found that P-value of GELMGPD is greater than that in each case of PLD and GELMPD. Hence, it is expected to be a better alternative to the PLD of Sankaran and GELMPD of Sah and Mishra for similar types of discrete data-sets which are negative binomial in nature. It is also observed that GELMGPD gives much more significant result when the value of is negative.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Performance Comparison of Web Backend And Database: A Case Study Of Node.JS, Golang and MySQL, MongoDB

2019 ◽  
Vol 13 ◽  
Author(s):  
Faried Effendy ◽  
Taufik ◽  
Bramantyo Adhilaksono
Keyword(s):  
Response Time ◽  
Open Source ◽  
Poisson Distribution ◽  
Mobile Application ◽  
Web Applications ◽  
Performance Comparison ◽  
Memory Usage ◽  
Data Traffic ◽  
Cpu Utilization

: Substantial research has been conducted to compare web servers or to compare databases, but very limited research combines the two. Node.js and Golang (Go) are popular platforms for both web and mobile application back-ends, whereas MySQL and Go are among the best open source databases with different characters. Using MySQL and MongoDB as databases, this study aims to compare the performance of Go and Node.js as web applications back-end regarding response time, CPU utilization, and memory usage. To simulate the actual web server workload, the flow of data traffic on the server follows the Poisson distribution. The result shows that the combination of Go and MySQL is superior in CPU utilization and memory usage, while the Node.js and MySQL combination is superior in response time.

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