arXiv subjects

Ishfaq Shah Ahmad

Publications and source records attributed to Ishfaq Shah Ahmad.

3 recordsLinked to original sources

arXiv2019

A New Mixed Generalized Negative Binomial Distribution

In this article, a generalized version of Negative binomial-beta exponential distribution with five parameters have been introduced. Some interesting submodels have been derived from it. A comprehensive mathematical treatment of proposed distribution is being provided. Various expressions like that of moment generating function, moments are derived. The model parameters are estimated by the maximum likelihood method. Finally, the application of proposed distribution is carried out on one sample of automobile insurance data.

math.ST↗

arXiv2019

Negative binomial-reciprocal inverse Gaussian distribution: Statistical properties with applications

In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some important properties not only in actuarial science but in other fields as well where overdispersion pattern is seen. Some basic properties including recurrence relation of probabilities for computation of successive probabilities have been discussed. In its compound version, when the claims are absolutely continuous, an integral equation for the probability density function is discussed. Brief discussion about extension of univariate version have also been done to its respective multivariate version. parameters involved in the model have been estimated by Maximum Likelihood Estimation technique. Applications of the proposed distribution are carried out by taking two real count data sets. The result shown that the negative binomial-reciprocal inverse Gaussian distribution gives better fit when compared to the Poisson and negative binomial distributions.

stat.ME↗

arXiv2018

A New Count Regression Model including Gauss Hypergeometric Function with an application to model demand of health services

In this paper, an alternative count distribution suitable for modeling over dispersed, zero vertex unimodality and monotonically decreasing data sets. Though the proposed probability model includes Gauss Hypergeometric special function, it possesses simple and closed expressions for various distributional characteristics. An application to count regression modeling using a well-known data set from the National Medical Expenditure Survey is discussed by considering the length of stay in hospitalization as a dependent variable and following the proposed count model. We compare our result with the classical Negative Binomial regression model and recently proposed Uniform Poisson regression model.

math.ST↗