相关论文: On the cumulative distribution function of the var…
The sum of correlated gamma random variables appears in the analysis of many wireless communications systems, e.g. in systems under Nakagami-m fading. In this Letter we obtain exact expressions for the probability density function (PDF) and…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
The Weibull--like distributions form a large class of probability distributions that belong to the domain of attraction for the maxima of the Gumbel law. Besides the Weibull distribution, it includes important distributions as the Gamma…
The distribution function of the sum $Z$ of two standard normally distributed random variables $X$ and $Y$ is computed with the concept of copulas to model the dependency between $X$ and $Y$. By using implicit copulas such as the Gauss- or…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
An integral over the interval $(0,\pi)$ is given for the cumulative distribution function of a sum of independent gamma random variables with different scale and shape parameters. The cumulative distribution function of a positive definite…
The aim of this note is to prove the inversion formula, which can be used to compute the Levi measure of an infinitely divisible distribution from its characteristic function. Obtained formula is similar to the well-known inversion formula…
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…
We consider estimating the proportion of random variables for two types of composite null hypotheses: (i) the means of the random variables belonging to a non-empty, bounded interval; (ii) the means of the random variables belonging to an…
In this paper we introduce a new probability distribution on (0,1), associated with the I-function, namely, the I-function distribution. This distribution generalizes several known distributions with positive support. It is also shown that…
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…
Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly…
The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformation of a random variable with the standard normal…
For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are…
This paper offers a mathematical invention that shows how to convert integrated quantiles, which often appear in risk measures, into integrated cumulative distribution functions, which are technically more tractable from various…
We provide theoretical error bounds for the accurate numerical computation of the quantile function given the characteristic function of a continuous random variable. We show theoretically and empirically that the numerical error of the…
The statistical distribution of the ratio of two normal random variables is characterized by its heavy-tailed nature and absence of finite moments. The shape of its density function is highly variable, capable of exhibiting unimodal or…
In [11] it has been proved some variational formula on the Legendre-Fenchel transform of the cumulant generating function (the Cram\'er function) of Rademacher series with coefficients in the space $\ell^1$. In this paper we show a…
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…
This paper presents properties and approximations of a random variable based on the zero-order modified Bessel function that results from the compounding of a zero-mean Gaussian with a $\chi^2_1$-distributed variance. This family of…