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

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.

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.

A new generalization of the logarithmic series distribution

2014 ◽  
Vol 51 (1) ◽  
pp. 41-49
Author(s):  
A. Mishra
Keyword(s):  
Method Of Moments ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Generalized Negative Binomial Distribution ◽  
Logarithmic Series Distribution ◽  
Logarithmic Series ◽  
Limiting Case ◽  
First Four Moments

A new generalization of the logarithmic series distribution has been obtained as a limiting case of the zero-truncated Mishra’s [10] generalized negative binomial distribution (GNBD). This distribution has an advantage over the Mishra’s [9] quasi logarithmic series distribution (QLSD) as its moments appear in compact forms unlike the QLSD. This makes the estimation of parameters easier by the method of moments. The first four moments of this distribution have been obtained and the distribution has been fitted to some well known data-sets to test its goodness of fit.

Patterns of macroparasite aggregation in wildlife host populations

Parasitology ◽  
1998 ◽  
Vol 117 (6) ◽  
pp. 597-610 ◽  
Author(s):  
D. J. SHAW ◽  
B. T. GRENFELL ◽  
A. P. DOBSON
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Data Sets ◽  
Frequency Distributions ◽  
System A ◽  
Host Sex ◽  
Host Parasite

Frequency distributions from 49 published wildlife host–macroparasite systems were analysed by maximum likelihood for goodness of fit to the negative binomial distribution. In 45 of the 49 (90%) data-sets, the negative binomial distribution provided a statistically satisfactory fit. In the other 4 data-sets the negative binomial distribution still provided a better fit than the Poisson distribution, and only 1 of the data-sets fitted the Poisson distribution. The degree of aggregation was large, with 43 of the 49 data-sets having an estimated k of less than 1. From these 49 data-sets, 22 subsets of host data were available (i.e. host data could be divided by either host sex, age, where or when hosts were sampled). In 11 of these 22 subsets there was significant variation in the degree of aggregation between host subsets of the same host–parasite system. A common k estimate was always larger than that obtained with all the host data considered together. These results indicate that lumping host data can hide important variations in aggregation between hosts and can exaggerate the true degree of aggregation. Wherever possible common k estimates should be used to estimate the degree of aggregation. In addition, significant differences in the degree of aggregation between subgroups of host data, were generally associated with significant differences in both mean parasite burdens and the prevalence of infection.

Analysis of generalized Poisson distributions associated with higher Landau levels

2015 ◽  
Vol 18 (04) ◽  
pp. 1550028 ◽  
Author(s):  
Nizar Demni ◽  
Zouhair Mouayn
Keyword(s):  
Probability Distribution ◽  
Characteristic Function ◽  
Poisson Distribution ◽  
Landau Level ◽  
Mass Function ◽  
Probability Mass Function ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Generalized Poisson ◽  
Probability Mass

To a higher Landau level corresponds a generalized Poisson distribution arising from generalized coherent states. In this paper, we write down the atomic decomposition of this probability distribution and express its probability mass function as a [Formula: see text]-hypergeometric polynomial. Then, we prove that it is not infinitely divisible in contrast with the Poisson distribution corresponding to the lowest Landau level. We also derive a Lévy–Khintchine-type representation of its characteristic function when the latter does not vanish and deduce that the representative measure is a quasi-Lévy measure. By considering the total variation of this last measure, we obtain the characteristic function of a new infinitely divisible discrete probability distribution for which we also compute the probability mass function.

scholarly journals Geometric Regression for Modelling Count Data on the Time-to-First Antenatal Care Visit

2020 ◽  
Vol 23 (1) ◽  
pp. 35-57
Author(s):  
Zainab Mohammed Darwish Al-Balushi ◽  
◽  
M. Mazharul Islam ◽  
Keyword(s):  
Antenatal Care ◽  
Regression Model ◽  
Count Data ◽  
Negative Binomial ◽  
Geometric Distribution ◽  
Discrete Distribution ◽  
Mass Function ◽  
Probability Mass Function ◽  
Antenatal Care Visit ◽  
Care Visit

Geometric distribution belongs to the family of discrete distribution that deals with the count of trail needed for first occurrence or success of any event. However, little attention has been paid in applying the GLM for the geometric distribution, which has a very simple form for its probability mass function with a single parameter. In this study, an attempt has been made to introduce geometric regression for modelling the count data. We have illustrated the suitability of the geometric regression model for analyzing the count data on time to first antenatal care visit that displayed under-dispersion, and the results were compared with Poisson and negative binomial regressions. We conclude that the geometric regression model may provide a flexible model for fitting count data sets which may present over-dispersion or under-dispersion, and the model may serve as an alternative model to the very familiar Poisson and negative binomial models for modelling count data.

scholarly journals A discrete Ramos-Louzada distribution for asymmetric and over-dispersed data with leptokurtic-shaped: Properties and various estimation techniques with inference

2022 ◽  
Vol 7 (2) ◽  
pp. 1726-1741
Author(s):  
Ahmed Sedky Eldeeb ◽  
◽  
Muhammad Ahsan-ul-Haq ◽  
Mohamed. S. Eliwa ◽  
◽  
...  
Keyword(s):  
Count Data ◽  
Discrete Distribution ◽  
Real Data ◽  
Mass Function ◽  
Probability Mass Function ◽  
Data Sets ◽  
Estimation Techniques ◽  
Proposed Model ◽  
Probability Mass ◽  
Von Mises

<abstract> <p>In this paper, a flexible probability mass function is proposed for modeling count data, especially, asymmetric, and over-dispersed observations. Some of its distributional properties are investigated. It is found that all its statistical and reliability properties can be expressed in explicit forms which makes the proposed model useful in time series and regression analysis. Different estimation approaches including maximum likelihood, moments, least squares, Andersonӳ-Darling, Cramer von-Mises, and maximum product of spacing estimator, are derived to get the best estimator for the real data. The estimation performance of these estimation techniques is assessed via a comprehensive simulation study. The flexibility of the new discrete distribution is assessed using four distinctive real data sets ԣoronavirus-flood peaks-forest fire-Leukemia? Finally, the new probabilistic model can serve as an alternative distribution to other competitive distributions available in the literature for modeling count data.</p> </abstract>

scholarly journals A finite form for the wrapped Poisson distribution

1992 ◽  
Vol 24 (01) ◽  
pp. 221-222 ◽  
Author(s):  
Frank Ball ◽  
Paul Blackwell
Keyword(s):  
Poisson Distribution ◽  
Mass Function ◽  
Probability Mass Function ◽  
Finite Form ◽  
Probabilistic Proof ◽  
Probability Mass

We give a finite form for the probability mass function of the wrapped Poisson distribution, together with a probabilistic proof. We also describe briefly its connection with existing results.

Generalized Hypergeometric Factorial Moment Distribution of Order k

2000 ◽  
Vol 50 (1-2) ◽  
pp. 71-78 ◽  
Author(s):  
C. Satheesh Kumar ◽  
T. S. K. Moothathu
Keyword(s):  
Negative Binomial ◽  
Factorial Moment ◽  
Mass Function ◽  
Discrete Distributions ◽  
Probability Mass Function ◽  
Factorial Moments ◽  
Point Distribution ◽  
Moment Distribution ◽  
Special Cases ◽  
Probability Mass

Here we introduce the generalized hypergeometric functional moment distribution of order k (GHFMD (k)) in the distribution of the random sum [Formula: see text] having Hira no's k-point distribution, where N, independent of X j's, has the generalized hypergeomet ric factorial moment distribution. Well-known discrete distributions of order k such as cluster binomial, cluster negative binomial and extended Poisson are shown to be special cases of GHFMD(k). The probability mass function, recurrence relations for probabilities and factorial moments of GHFMD (k) are found out. The beta or the gamma mixture of GHFMD (k) is shown to be a GHFMD (k). Finally GHFMD (k) is obtained as a limit of another GHFMD (k). AMS (2000) Subject Classification: Primary 60E05, 60E10; Secondary 33C20.

scholarly journals A finite form for the wrapped Poisson distribution

1992 ◽  
Vol 24 (1) ◽  
pp. 221-222 ◽  
Author(s):  
Frank Ball ◽  
Paul Blackwell
Keyword(s):  
Poisson Distribution ◽  
Mass Function ◽  
Probability Mass Function ◽  
Finite Form ◽  
Probabilistic Proof ◽  
Probability Mass

We give a finite form for the probability mass function of the wrapped Poisson distribution, together with a probabilistic proof. We also describe briefly its connection with existing results.

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