In this correspondence, we point out two typographical errors in Chai and Tjhung’s paper and we offer the correct formula of the unified Laguerre polynomial-seriesbased cumulative distribution function (cdf) for small-scale fading distributions. A Laguerre polynomial-series-based cdf formula for non-central chi-square distribution is also provided as a special case of our unified cdf result.

1 General case 1.1 Cumulative distribution function 1.2 A counterexample 1.3 Normally distributed and independent 2 Bivariate case 3 Affine transformation 4 Geometric interpretation 5 Correlations and independence 6 Higher moments 7 Conditional distributions 8 Fisher information matrix 9 Kullback-Leibler divergence 10 Estimation of parameters 11 Entropy 12 Multivariate normality tests 13 Drawin...

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 ...

We propose a new kernel estimation of the cumulative distribution function based on transformation and on bias reducing techniques. We derive the optimal bandwidth that minimises the asymptotic integrated mean squared error. The simulation results show that our proposed kernel estimation improves alternative approaches when the variable has an extreme value distribution with heavy tail and the ...

In this paper we show how the distribution of the discrete Choquet integral can be analytically computed. The advantage of having an analytical expression is that the value of the cumulative distribution function (cdf) can be computed exactly for the Choquet. We also derive an expression for the density of the Ordered Weighted Average (OWA) operator, which is a special case of the Choquet.

abstract agricultural scientists have developed considerable interest in modeling and generation of rainfall as new ways of analyzing rainfall data and assessing its impact on agriculture. a combination of markov chain and gamma distribution function is recognized as a simple approach and is demonstrated to be effective in generating daily rainfall data for many environments. thus the availabil...

It is well known that generalized models is attracting the attention of researchers in recent times because of their flexibilities. Particularly, the logistic model has been generalized and applied by many authors while the half logistic distribution has not recieve much attention in term of its generalization. In this paper, we considered a generalized form of half logistic model called type I...

The beta Weibull distribution was introduced by Famoye et al. (2005) and studied by these authors. However, they do not give explicit expressions for the moments. We now derive explicit closed form expressions for the cumulative distribution function and for the moments of this distribution. We also give an asymptotic expansion for the moment generating function. Further, we discuss maximum lik...