Related papers: The I-Function Distribution and its Extensions
A new discrete distribution has been proposed as a discrete analogue of the two sided power distribution [Van Drop, J. R. and Kotz, S. (2002a). A novel extension of the triangular distribution and its parameter estimation, Journal of the…
We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
A new characterization of the multivariate so-called "quasi-Gaussian distribution" (the authors dared to coin a new term) by means of independence their Cartesian and polar coordinates proposed. The authors try to show that these…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
In this article, we study the distribution of values of Dirichlet $L$-functions, the distribution of values of the random models for Dirichlet $L$-functions, and the discrepancy between these two kinds of distributions. For each question,…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
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…
A probability inequality is proved for n-fold convolutions of a smooth cumulative distribution function on (0,infinity)x...x(0,infinity), which is multivariate totally positive of order 2 (MTP2). This inequality is better than an inequality…
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
A new class of probability distributions closely connected to generalized hyperbolic distributions is introduced. It is more adapted to study the distributions of sums of random number of random variables. The properties of these…
We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…
In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging…
A new characterization for power function distributions is obtained which is based on products of order statistics. This result may be considered as a generalization of some recent results for contractions. We note that in this new result…
Using a recently derived integral in terms of elementary functions, we derive new asymptotic expansions of the normal inverse Gaussian cumulative distribution function. One of the asymptotic representations is in terms of the normal…
We propose a two-parameter bounded probability distribution called the extended power distribution. This distribution on $(0, 1)$ is similar to the beta distribution, however there are some advantages which we explore. We define the moments…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
We study arithmetic distribution relations and the inverse function theorem in algebraic and arithmetic geometry, with an emphasis on versions that can be applied uniformly across families of varieties and maps. In particular, we prove two…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…