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If g and G are the pdf and the cdf of a distribution symmetric around 0 then the pdf 2g(u)G(λ
u) is said to define a skew distribution. In this paper, we provide a mathematical treatment of the skew distributions when
g and G are taken to come from one of Pearson type II, Pearson type VII or the generalized t distribution.
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In this paper, we introduce a new extension of the power Lindley distribution, called the exponentiated generalized power Lindley distribution. Several mathematical properties of the new model such as the shapes of the density and hazard rate functions, the quantile function, moments, mean deviations, Bonferroni and Lorenz curves and order statistics are derived.Moreover, we discuss the parameter estimation of the new distribution using the maximum likelihood and diagonally weighted least squares methods. A simulation study is performed to evaluate the estimators. We use two real data sets to illustrate the applicability of the new model. Empirical findings show that the proposed model provides better fits than some other well-known extensions of Lindley distributions. 相似文献
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The known estimation and simulation methods for multivariate t distributions are reviewed. A review of selected applications is also provided. We believe that this review will serve as
an important reference and encourage further research activities in the area. 相似文献
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Saralees Nadarajah 《Mathematical Methods in the Applied Sciences》2008,31(1):35-44
A new Pareto distribution is introduced for pooling knowledge about classical systems. It takes the form of the product of two Pareto probability density functions (pdfs). Various structural properties of this distribution are derived, including its cumulative distribution function (cdf), moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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We give the cumulative distribution function of $M_n$ , the maximum of a sequence of n observations from a first order moving average. Solutions are first given in terms of repeated integrals and then for the case, where the underlying independent random variables have an absolutely continuous probability density function. When the correlation is positive, $P( M_n \leq x ) \ =\ \sum\limits _{j=1}^{\infty } \beta _{j, x} \ \nu _{j, x}^{n},$ where $\{\nu _{j, x}\}$ are the eigenvalues (singular values) of a Fredholm kernel and $\beta _{j, x}$ are some coefficients determined later. A similar result is given when the correlation is negative. The result is analogous to large deviations expansions for estimates, since the maximum need not be standardized to have a limit. For the continuous case the integral equations for the left and right eigenfunctions are converted to first order linear differential equations. The eigenvalues satisfy an equation of the form $\sum\limits _{i=1}^{\infty } w_i ( \lambda -\theta _i )^{-1}=\lambda -\theta _0$ for certain known weights $\{ w_i\}$ and eigenvalues $\{ \theta _i\}$ of a given matrix. This can be solved by truncating the sum to an increasing number of terms. 相似文献
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Christopher?S.?Withers Saralees?NadarajahEmail author 《Methodology and Computing in Applied Probability》2016,18(3):911-920
Withers and Nadarajah (Stat Pap 51:247–257; 2010) gave simple Edgeworth-type expansions for log densities of univariate estimates whose cumulants satisfy standard expansions. Here, we extend the Edgeworth-type expansions for multivariate estimates with coefficients expressed in terms of Bell polynomials. Their advantage over the usual Edgeworth expansion for the density is that the kth term is a polynomial of degree only k + 2, not 3k. Their advantage over those in Takemura and Takeuchi [Sankhyā, A, 50, 1998, 111-136] is computational efficiency 相似文献