Related papers: On the gamma difference distribution
Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize…
The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and distributional…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…
The gamma density function is usually defined in interval between zero and infinity. This paper introduces an upper and a lower boundary to this distribution. The parameters which characterize the truncated gamma distribution are evaluated.…
In this article, we develop Stein characterization for two-sided tempered stable distribution. Stein characterizations for normal, gamma, Laplace, and variance-gamma distributions already known in the literature follow easily. One can also…
Available in the literature are properties which characterize the gamma distribution via independence of two appropriately chosen statistics. Well-known is the classical result when one of the statistics is the sample mean and the other one…
The generalized hyperbolic (GH) distributions form a five parameter family of probability distributions that includes many standard distributions as special or limiting cases, such as the generalized inverse Gaussian distribution, Student's…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
General hypergeometric distribution (GHGD) definition: from a finite space $N$ containing $n$ elements, randomly select totally $T$ subsets $M_i$ (each contains $m_i$ elements, $1 \geq i \geq T$), what is the probability that exactly $x$…
The gamma distribution is a useful model for small area prediction of a skewed response variable. We study the use of the gamma distribution for small area prediction. We emphasize a model, called the gamma-gamma model, in which the area…
We obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein…
The generalized gamma distribution shows up in many problems related to engineering, hydrology as well as survival analysis. Earlier work has been done that estimated the deviation of the exponential and the Weibull distribution from…
Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a…
This article aims to introduced a new distribution named as extended xgamma (EXg) distribution. This generalization is derived from xgamma distribution (Xg), a special finite mixture of exponential and gamma distributions [see, Sen et al.…
In this article, we obtain the exact distribution of a linear combination of bilateral gamma (BG) random variables (r.v.s). Next, we discuss the distributional properties of the linear combination of BG r.v.s, including probability density…
The break-by-one gamma distribution has a probability density function resembling the Schechter function, but with the small-argument behavior modified so it is normalizable in commonly arising cases where the Schechter function is not. Its…
The theory of normal variance mixture distributions is used to provide elementary derivations of closed-form expressions for the definite integrals $\int_0^\infty x^{-2\nu}\cos(bx)\gamma(\nu,\alpha x^2)\,\mathrm{d}x$ (for $\nu>1/2$, $b>0$…
We examine the Gaussian hypergeometric beta distribution and look at the effect of having an additional term in the density kernel relative to the standard beta distribution. We reparameterise and classify this distribution into left and…
We propose a Stein characterization of the Kummer distribution on (0, $\infty$). This result follows from our observation that the density of the Kummer distribution satisfies a certain differential equation, leading to a solution of the…