arXiv subjects

Deepesh Bhati

Publications and source records attributed to Deepesh Bhati.

12 recordsLinked to original sources

arXiv2026

A Stein Characterization-type Omnibus Tests for the Discrete Pareto Distribution

The discrete Pareto (or Zeta, Zipf) distribution, arises naturally in modeling rank-frequency data across diverse fields such as linguistics, demography, biology, and computer science. Despite its widespread applicability, goodness-of-fit testing for the discrete Pareto distribution remains underdeveloped, particularly in the presence of heavy tails and infinite support. This article introduces a novel goodness-of-fit test based on a new Stein-type characterization of the discrete Pareto distribution, formulated using its probability generating function. The proposed method is applicable even when the shape parameter is unknown and avoids binning or smoothing techniques. We study the asymptotic properties of the test and assess its empirical size and power through extensive simulation experiments. The results show that the proposed test either outperforms or matches the performance of existing method across various alternatives. Applications to real datasets are provided to demonstrate its practical relevance and robustness.

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arXiv2026

Laplace Transform driven Stein-type Goodness-of-fit Tests for Pareto Distribution

The Pareto distribution plays a crucial role in various disciplines, necessitating robust goodness-of-fit tests for its validation. This article introduces a novel tests based on Stein's characterization and the Laplace transform, offering a fresh perspective on model assessment. We establish the asymptotic properties of the proposed test and evaluate its empirical performance against existing methods in terms of size and power. Our findings demonstrate that the new test often outperforms or performs comparably to established tests. In addition, real data applications illustrate its practical utility.

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arXiv2022

A Copula-Based family of Bivariate Composite Models for Claim Severity Modelling

In this paper, we consider bivariate composite models for modeling jointly different types of claims and their associated costs in a flexible manner. For expository purposes, the Gumbel copula is paired with the composite Weibull-Inverse Weibull, Paralogistic-Inverse Weibull, and Inverse Burr-Inverse Weibull marginal models. The resulting bivariate copula-based composite models are fitted on motor insurance bodily injury and property damage data from a European motor insurance company and their parameters are estimated via the inference functions for margins method.

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arXiv2022

Composite Lognormal-T regression models with varying threshold and its insurance application

Composite probability models have shown very promising results for modeling claim severity data comprised of small, moderate, and large losses. In this paper, we introduce three classes of parametric composite regression models with a varying threshold. We consider the Lognormal distribution for the head and the Burr, the Stoppa and the generalized log-Moyal (GlogM) distributions for the tail part of the composite family. Further, the Mode-Matching procedure has been utilized for the composition of the two densities. To capture the heterogeneous behavior of the policyholder's characteristics, covariates are introduced into the scale parameter of the tail distribution. Finally, the applicability of the proposed models has been shown using a real-world insurance data set.

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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.

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arXiv2018

Jackknife empirical likelihood based inference for Probability weighted moments

In the present article, we discuss jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) based inference for finding confidence intervals for probability weighted moment (PWM). We obtain the asymptotic distribution of the JEL ratio and AJEL ratio statistics. We compare the performance of the proposed confidence intervals with recently developed methods in terms of coverage probability and average length. We also develop JEL and AJEL based test for PWM and study it properties. Finally we illustrate our method using rainfall data of Indian states.

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arXiv2016

Analysis of Count Data by Transmuted Geometric Distribution

Transmuted geometric distribution (TGD) was recently introduced and investigated by Chakraborty and Bhati (2016). This is a flexible extension of geometric distribution having an additional parameter that determines its zero inflation as well as the tail length. In the present article we further study this distribution for some of its reliability, stochastic ordering and parameter estimation properties. In parameter estimation among others we discuss an EM algorithm and the performance of estimators is evaluated through extensive simulation. For assessing the statistical significance of additional parameter, Likelihood ratio test, the Rao's score tests and the Wald's test are developed and its empirical power via simulation were compared. We have demonstrate two applications of (TGD) in modeling real life count data.

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arXiv2016

An Alternative Discrete Skew Logistic Distribution

In this paper, an alternative Discrete skew Logistic distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The properties of the distribution are explored and it is compared to a discrete distribution defined on integers recently proposed in the literature. The estimation of its parameters are discussed, with particular focus on the maximum likelihood method and the method of proportion, which is particularly suitable for such a discrete model. A Monte Carlo simulation study is carried out to assess the statistical properties of these inferential techniques. Application of the proposed model to a real life data is given as well.

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arXiv2016

A new 3-parameter extension of generalized lindley distribution

Here, we introduce a new class of Lindley generated distributions which results in more flexible model with increasing failure rate (IFR), decreasing failure rate(DFR) and up-side down hazard functions for different choices of parametric values. We explore, various distributional properties including limiting distribution of extreme order statistics explored. Maximum likelihood estimators and the confidence intervals of the parameters are obtained. The applicability of the proposed distribution is shown through modelling two sets of real data on bladder cancer patients and waiting time in a queue. Further, we carry out stress-strength analysis for applying the model in system reliability studies.

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arXiv2015

Weighted geometric distribution with a new characterisation of geometric distribution

In this paper, we introduce a new generalization of geometric distribution which can also viewed as discrete analogue of weighted exponential distribution introduced by Gupta and Kundu(2009). We study some basic distributional properties like moments, generating functions, hazard function followed by different methods of estimation of the parameters. Characterization of Geometric distribution have also been presented. Finally, we examine the model with real data sets.

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arXiv2015

A New Count Model Generated from Mixed Poisson Transmuted Exponential Family with an application to Health Care Data

In this paper, a new mixed Poisson distribution is introduced. This new distribution is obtained by utilizing mixing process, with Poisson distribution as mixed distribution and Transmuted Exponential distribution as mixing distribution. Some distributional properties like unimodality, moments, over-dispersion, Taylor series expansion of proposed model are studied. Estimation of the parameters using method of moments, method of moments and proportion and maximum likelihood estimation along with data fitting experiment to show its advantage over some existing distribution. Further, an actuarial applications in context of aggregate claim distribution is discussed. Finally, we discuss a count regression model based on proposed distribution and its usefulness over some well established model.

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arXiv2014

On Lindley-Exponential Distribution: Properties and Application

In this paper, we introduce a new distribution generated by Lindley random variable which offers a more flexible model for modelling lifetime data. Various statistical properties like distribution function, survival function, moments, entropy, and limiting distribution of extreme order statistics are established. Inference for a random sample from the proposed distribution is investigated and maximum likelihood estimation method is used for estimating parameters of this distribution. The applicability of the proposed distribution is shown through real data sets.

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