This paper introduces a comprehensive C++ software package, HatchFrac, for stochastic modeling of fracture networks in two and three dimensions. The inverse cumulative distribution function (CDF) acceptance–rejection methods are applied to generate random variables from the distributions commonly used discrete network (DFN) modeling. multilayer perceptron (MLP) machine learning approach, combin...

In this article, a new distribution having three called Modified Generalized Exponential Distribution is proposed. Important statistical properties of the proposed model like survival function, hazard rate probability density function (PDF), cumulative (CDF), quantile skewness, and kurtosis are discussed here. Least Square Estimation (LSE), Cramer- Von Mises (CVM) Maximum Likelihood estimators ...

Abstract In this paper, a new Poisson area-biased Ailamujia distribution has been formulated to analyse count data. It was created by combining two distributions: the and distributions, using compounding technique. Several distributional properties of were studied. Its ageing characteristics determined expressed explicitly. A variety diagrams used demonstrate probability mass function (pmf) cum...

In this paper, closed-form expressions for probability density function (PDF) and cumulative distribution function (CDF) of the signal-to-interference ratio (SIR) at the output of the triple selection combining (SC) receiver over correlated Weibull fading channels in the presence of correlated cochannel interference (CCI) are derived. These expressions are used to study wireless system performa...

In this article, we have suggested the three-parameter half-Cauchy Chen distribution which has been derived by compounding a continuous with family of distribution. The hazard rate function (HRF), quantile function, reversed survival cumulative (CDF), probability density (PDF), kurtosis, and skewness are some its statistical properties characteristics that explored. Utilizing methods LSE, CVM, ...

I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of this heavy tail Lambert W × F X random variable depends on a tail parameter δ ≥ 0: for δ = 0, Y ≡ X, for δ > 0 Y has heavier tails than X. For X being Gaussian it reduces to Tukey's h distribution. The Lambert W function provides an explicit inverse transformation...

The cumulative distribution function of the non-central chi-square χn′2(λ) n degrees freedom possesses an integral representation. Here we rewrite this in terms a lower incomplete gamma applying two second mean-value theorems for definite integrals, which are Bonnet type and Okamura’s variant du Bois–Reymond theorem. Related results exposed concerning small argument cases (CDF) their asymptotic...

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 the cumulative distribution function (CDF) of the sum of arbitrarily correlated gamma variables in terms of certain Lauricella functions. Index Terms Gamma ...

The cumulative distribution function (CDF) of the T-X family is given by R{W(F(x))}, where R is the CDF of a random variable T, F is the CDF of X and W is an increasing function defined on [0, 1] having the support of T as its range. This family provides a new method of generating univariate distributions. Different choices of the R, F and W functions naturally lead to different families of dis...

The probability distribution of precipitation amount strongly depends on geography, climate zone, and time scale considered. Closed-form parametric distributions are not sufficiently flexible to provide accurate universal models for over different scales. In this paper we derive non-parametric estimates the cumulative function (CDF) wet periods. CDF obtained by integrating kernel density estima...