In this paper, some various families constructed from the logit of the generalized Beta, Beta، Kumar, generalized Gamma, Gamma, Weibull, log gamma and Logistic Distributions are reviewed. Then a general family of Distributions generated from the logit of the Normal Distribution is proposed. A special case of this family, Normal-Uniform Distribution, is defined and studied. Various properties of the Distribution are also explored. The maximum likelihood and minimum spacings estimators of the parameters of this Distribution are obtained. Finally, the new Distribution is effectively used to analysis a real survival data set.

To View The Abstract, Please Click On PDF File.

In this paper, we discuss a generalization of Balakrishnan skew Normal Distribution with two parameters that contains the skew-Normal, the Balakrishnan skew-Normal and the two-parameter generalized skew-Normal Distributions as special cases. Furthermore, we establish some useful properties and two extensions of this Distribution.

In this article new generalization of half-Normal Distribution as the half generalized Normal Distribution is introduced. ‎This Distribution, contains the half-Normal Distribution as special case.‎ We provide mathematical properties of this Distribution. We also derive the pdf, cdf, -th moment, the asymmetry and kurtosis coefficients and the moment generating function. We discuss some inferential aspects related to the maximum likelihood estimation. Finally we illustrate the flexibility of this type of Distribution with applications to real data sets.

Consider an exchangeable Normal vector with parameters μ, σ2, and ρ. On the basis of a vector observation some tests about these parameters are found and their properties are discussed. A simulation study for these tests and a few nonparametric tests are presented. Some advantages and disadvantages of these tests are discussed and a few applications are given.

Objective Investors typically seek to strike the optimal balance between potential returns and associated risks in their trades. Various models have been presented to choose the optimal portfolio using different approaches. one of these methods is based on the statistical Distribution of asset return. In these methods, the type of Distribution of returns is first identified, and a suitable portfolio selection method is then applied based on this identified Distribution type. This study compares the effectiveness of the mean-absolute deviation-entropy model utilizing both Skew-Normal Distribution and Skew-Laplace-Normal Distribution for constructing an optimal portfolio in the Tehran Stock Exchange over 36 months from April 2018 to March 2020.   Methods The data used in this study comprises the monthly returns of 181 companies listed on the Tehran Stock Exchange. These returns were gathered from a statistical population of 338 members utilizing Morgan's table and Cochran’s formula. After fitting density functions for Skew-Normal and Skew-Laplace-Normal Distributions to the returns, maximum likelihood estimates were obtained using the Stats package and the optim Function in R software. The reliability of these estimates was then checked using bootstrap sampling with 1,000 repetitions. Subsequently, relationships corresponding to the mathematical expectation of return Distribution and the objective function representing the risk of absolute deviation were estimated using numerical methods. Therefore, this paper aimed to propose a multi-objective optimization model, namely a mean-absolute deviation-entropy model for portfolio optimization by using a goal-programming approach based on Skew-Normal Distribution and Skew-Laplace-Normal Distribution. The objective functions of the model were to maximize the mean return, minimize the absolute deviation, and maximize the entropy of the portfolio.   Results It can be inferred from the observed values ​​of the descriptive statistics of the monthly stock returns corresponding to the stock exchange symbols that some stocks have different skewness and kurtosis values ​​compared to the Normal Distribution. For example, The symbol "Shepna" exhibits negative skewness, indicating a left-skewed Distribution. Similarly, the Distribution of the "Basama" symbol exceeds the Normal Distribution. These instances suggest that the Normal Distribution is inadequate for describing monthly return Distributions. Instead, Distributions with parameters should be employed to account for skewness and kurtosis. According to the obtained results, the model utilizing the Skew- Laplace- Normal Distribution has a higher performance ratio than the model based on the Skew-Normal Distribution.   Conclusion The reason for this superiority, where the model utilizing the Skew-Laplace-Normal Distribution outperforms the model based on the Skew-Normal Distribution, is the incorporation of both skewness and kurtosis criteria within the former. Additionally, upon analyzing the descriptive statistics of the symbols, it's evident that the kurtosis of most stock symbols is substantial. Therefore, integrating a combination of higher-order moments (skewness and kurtosis) along with entropy leads to enhanced performance.

In this paper, by conditioning on the matrix variate Normal Distribution (MVND) the construction of the matrix t-type family is considered, thus providing a new perspective of this family. Some important statistical characteristics are given. The presented t-type family is an extension to the work of Dickey [8]. A Bayes estimator for the column covariance matrix S of MVND is derived under Kullback Leibler divergence loss (KLDL). Further an application of the proposed result is given in the Bayesian context of the multivariate linear model. It is illustrated that the Bayes estimators of coefficient matrix under both SEL and KLDL are identical.

In this paper, a new generalization of the half-Normal Distribution which is called the perturbed half-Normal Distribution is introduced. The new Distribution belongs to a family of Distributions which includes the half-Normal Distribution along with an extra parameter to regulate skewness. The probability density function (pdf) is derived and some various properties of the new Distribution are obtained. The derived properties include the cumulative Distribution function (cdf), the rth moment, moment generating function, characteristic function, mean deviation about the mean and estimation of the parameters using the method of moments and maximum likelihood. Finally, the flexibility and potentiality of the new Distribution is illustrated in an application to two real data sets.