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The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
In this paper three new characterizing theorems of exponential distribution are presented. They are based on equidistribution of some functions of order statistics. All of them include the median of sample of size three.
Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…
Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
In this paper, insight is given in the techniques used to compute asymptotic expansions. In a broad fashion the technique is described. Most of the results apply to the paper "An expansion for the maximum likelihood estimator and its…
We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
Let $X_1, X_2,\ldots, X_n$ be $n$ independent and identically distributed random variables, here $n \geq 2.$ Let $X_{(1)}, X_{(2)}, \ldots, X_{(n)}$ be the order statistics of $X_1, X_2,..., X_n.$ In this note we proved that: (I) If $X_1,…
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…
Semiparametric exponential family proposed by Ning et al. (2017) is an extension of the parametric exponential family to the case with a nonparametric base measure function. Such a distribution family has potential application in some areas…
The present article studies survival analytic aspects of semiparametric copula dependence models with arbitrary univariate marginals. The underlying survival functions admit a representation via exponent measures which have an…
The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf)…
In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as beta-exponential and generalized Gompertz…
A new parameterization and algorithm are proposed for seeking the primary relative maximum of the likelihood function in the three-parameter lognormal distribution. The parameterization yields the dimension reduction of the three-parameter…
In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum…
Marshall and Olkin (1997, Biometrika, 84, 641 - 652) introduced a very powerful method to introduce an additional parameter to a class of continuous distribution functions and hence it brings more flexibility to the model. They have…
Probability distributions and densities are derived for the excess and deficiency of the intensity or instantaneous energy (quasi-static power) associated with a $p$-dimensional random vector field. Explicit expressions for the exact…