Related papers: The variance-gamma ratio distribution
We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…
Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
Approximate distributions for sum and difference of linearly correlated $\chi^{2}$ distributed random variables are derived. It is shown that they can be reduced to conveniently parametrized gamma and Variance-Gamma distributions,…
The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and Gamma subordinators with the two-parameters, $\alpha$ and…
This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…
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…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Several representations of the exact cdf of the sum of squares of n independent gamma-distributed random variables Xi are given, in particular by a series of gamma distribution functions. Using a characterization of the gamma distribution…
The poster presents an analytic formalism describing metric properties of undirected random graphs with arbitrary degree distributions and statistically uncorrelated (i.e. randomly connected) vertices. The formalism allows to calculate the…
Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…
Random models of evolution are instrumental in extracting rates of microscopic evolutionary mechanisms from empirical observations on genetic variation in genome sequences. In this context it is necessary to know the statistical properties…
The family of skew-symmetric distributions is a wide set of probability density functions obtained by combining in a suitable form a few components which are selectable quite freely provided some simple requirements are satisfied. Intense…
Let $ k >0 $ be an integer and $ Y $ a standard Gamma$(k)$ distributed random variable. Let $ X $ be an independent positive random variable with a density that is hyperbolically monotone (HM) of order $ k.$ Then $Y\cdot X$ and $Y/X $ both…
The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…
In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…
The distribution of the sum of r-th power of standard normal random variables is a generalization of the chi-squared distribution. In this paper, we represent the probability density function of the random variable by an one-dimensional…
If two random variables X and A are functionally related via f(X)=A for some strictly monotone continuously differentiable function f:R->R, the distribution of X may easily be computed from the distribution of A.
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…