A Generalised Exponential-Lindley Mixture of Poisson Distribution (original) (raw)
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On a Generalised Exponential-Lindley Mixture of Generalised Poisson Distribution
Nepalese journal of statistics, 2020
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.
On Poisson-Weighted Lindley Distribution and Its Applications
Journal of Scientific Research
In this paper the nature and behavior of its coefficient of variation, skewness, kurtosis and index of dispersion of Poisson- weighted Lindley distribution (P-WLD), a Poisson mixture of weighted Lindley distribution, have been proposed and the nature and behavior have been explained graphically. Maximum likelihood estimation has been discussed to estimate its parameters. Applications of the proposed distribution have been discussed and its goodness of fit has been compared with Poisson distribution (PD), Poisson-Lindley distribution (PLD), negative binomial distribution (NBD) and generalized Poisson-Lindley distribution (GPLD).
Pakistan Journal of Statistics and Operation Research
In this paper, a new mixture distribution for count data, namely the negative binomial-new generalized Lindley (NB-NGL) distribution is proposed. The NB-NGL distribution has four parameters, and is a flexible alternative for analyzing count data, especially when there is over-dispersion in the data. The proposed distribution has sub-models such as the negative binomial-Lindley (NB-L), negative binomial-gamma (NB-G), and negative binomial-exponential (NB-E) distributions as the special cases. Some properties of the proposed distribution are derived, i.e., the moments and order statistics density function. The unknown parameters of the NB-NGL distribution are estimated by using the maximum likelihood estimation. The results of the simulation study show that the maximum likelihood estimators give the parameter estimates close to the parameter when the sample is large. Application of NB-NGL distribution is carry out on three samples of medical data, industry data, and insurance data. Ba...
A Generalization of Generalized Poisson-Lindley Distribution and its Applications
Journal of Modern Applied Statistical Methods
In this paper we proposed a generalization of generalized Poisson-Lindley distribution which includes generalized Poisson-Lindley distribution, Poisson-Lindley distribution, Poisson- weighted Lindley distribution, negative binomialdistribution and geometric distribution as special cases. Statistical properties based on moments, maximum likelihood estimation and applications of the distribution have been discussed.
A New Generalized Poisson-Lindley Distribution: Applications and Properties
Austrian Journal of Statistics, 2015
A new generalized Poisson Lindley distribution is obtained by compounding Poissondistribution with two parameter generalised Lindley distribution. The new distribution isshown to be unimodal and over dispersed. This distribution has a tendency to accommodate right tail as well as for particular values of parameter the tail tends to zero at a faster rate. Various properties like cumulative distribution function, generating function, Moments etc. are derived. Knowledge about the parameters is obtained through Method of Moments, Maximum Likelihood Method and EM Algorithm. Moreover, an actuarial application in collective risk model is shown by considering the proposed distribution as primary and Exponential and Erlang as secondary distribution. The model is applied to real dataset and found to perform better than competing models.
FAMILY OF POISSON DISTRIBUTION AND ITS APPLICATION
The purpose of this paper is to introduce three discrete distributions named Poisson exponential distribution, Poisson size biased exponential distribution and size biased Poisson exponential distribution. These distributions apply to biological data sets, traffic datasets and thunderstorm datasets. These distributions are introduced with some of its basic properties including moments, coefficient of skewness and kurtosis are discussed. The method of moments and maximum likelihood estimation of the parameters of discrete PED, PSBED and SBPED are investigated. It is found that the reciprocal of MOM and MLE estimator is unbiased for the proposed distributions. Applications of the three models to different discrete data sets are compared with Poisson distribution, size biased Poisson distribution, size biased generalized Poisson distribution size biased geometric distribution and size biased Poisson lindley distribution to test their goodness of fit and the fit shows that the proposed distributions can be an important tool for modelling biological, traffic and other discrete data sets.
A weighted negative binomial Lindley distribution with applications to dispersed data
Anais da Academia Brasileira de Ciências
A new discrete distribution is introduced. The distribution involves the negative binomial and size biased negative binomial distributions as sub-models among others and it is a weighted version of the two parameter discrete Lindley distribution. The distribution has various interesting properties, such as bathtub shape hazard function along with increasing/decreasing hazard rate, positive skewness, symmetric behavior, and over-and under-dispersion. Moreover, it is self decomposable and infinitely divisible, which makes the proposed distribution well suited for count data modeling. Other properties are investigated, including probability generating function, ordinary moments, factorial moments, negative moments and characterization. Estimation of the model parameters is investigated by the methods of moments and maximum likelihood, and a performance of the estimators is assessed by a simulation study. The credibility of the proposed distribution over the negative binomial, Poisson and generalized Poisson distributions is discussed based on some test statistics and four real data sets.
Negative Binomial-Lindley Distribution and Its Application
Journal of Mathematics and Statistics, 2010
Problem statement: The modeling of claims count is one of the most important topics in actuarial theory and practice. Many attempts were implemented in expanding the classes of mixed and compound distributions, especially in the distribution of exponential family, resulting in a better fit on count data. In some cases, it is proven that mixed distributions, in particular mixed Poisson and mixed negative binomial, provided better fit compared to other distributions. Approach: In this study, we introduce a new mixed negative binomial distribution by mixing the distributions of negative binomial (r,p) and Lindley (θ), where the reparameterization of p = exp(-λ) is considered. Results: The closed form and the factorial moment of the new distribution, i.e., the negative binomial-Lindley distribution, are derived. In addition, the parameters estimation for negative binomial-Lindley via the method of moments (MME) and the Maximum Likelihood Estimation (MLE) are provided. Conclusion: The application of negative binomial-Lindley distribution is carried out on two samples of insurance data. Based on the results, it is shown that the negative binomial-Lindley provides a better fit compared to the Poisson and the negative binomial for count data where the probability at zero has a large value.
The complementary Poisson-Lindley class of distributions
International Journal of Advanced Statistics and Probability, 2015
This paper proposed a new general class of continuous lifetime distributions, which is a complementary to the Poisson-Lindley family proposed by Asgharzadeh et al. [3]. The new class is derived by compounding the maximum of a random number of independent and identically continuous distributed random variables, and Poisson-Lindley distribution. Several properties of the proposed class are discussed, including a formal proof of probability density, cumulative distribution, and reliability and hazard rate functions. The unknown parameters are estimated by the maximum likelihood method and the Fisher's information matrix elements are determined. Some sub-models of this class are investigated and studied in some details. Finally, a real data set is analyzed to illustrate the performance of new distributions.
A New Mixture Model from Generalized Poisson and Generalized Inverse Gaussian Distribution
Far East Journal of Theoretical Statistics, 2017
In this paper, we propose a new distribution for modeling count datasets with some unique characteristics, obtained by mixing the generalized Poisson distribution (GPD) and the generalized inverse Gaussian distribution (GIGD) and using the framework of the Lagrangian probability distribution. Some structural properties of the proposed new distribution are discussed. Parameter estimates are computed using the method of maximum likelihood. A real-life data set is used to examine the performance of the new distribution.