Tail Behavior and Limit Distribution of Maximum of Logarithmic General Error Distribution

Logarithmic general error distribution, an extension of the log-normal distribution, is proposed. Some interesting properties of the log GED are derived. These properties are applied to establish the asymptotic behavior of the ratio of probability densities and the ratio of the tails of the logarithmic general error and log-normal distributions, and to derive the asymptotic distribution of the partial maximum of an independent and identically distributed sequence obeying the log GED.     

The linear combination,product and ratio of Laplace random variables

The distributions of linear combinations, products and ratios of random variables arise in many areas of engineering. In this paper, the exact distributions of the linear combination α X+β Y, the product |X Y| and the ratio |X/Y| are derived when X and Y are independent Laplace random variables. The Laplace distribution, being the oldest model for continuous data, has been one of the most popular models for measurement errors in engineering.     

Confidence Intervals for Linear Combinations of Poisson Means

Parametric confidence intervals are given for linear combinations of the means of independent Poisson variables and for their continuous versions. The performance of the intervals is assessed using simulation. A real data set is used to compare the proposed intervals with known ones. The proposed intervals are shown to be superior to known ones and comparable to exact intervals.     

Extreme value models with application to drought data

Summary The exact distributions of the productXY are derived whenX andY are independent random variables and come from the extreme value distribution of Type I, the extreme value distribution of Type II or the extreme value distribution of Type III. Of the, six possible combinations, only three yield closed-form expressions for the distribution ofXY. A detailed application of the results is provided to drought data from Nebraska. The author would like to thank the referees and the Associate Editor for carefully reading the paper and for their great help in improving the paper.     

Correlation is first order independent of transformation

We show that the correlation between the estimates of two parameters is almost unchanged if they are each transformed in an arbitrary way. To be more specific, the correlation of two estimates is invariant (except for a possible sign change) up to a first order approximation, to smooth transformations of the estimates. There is a sign change if exactly one of the transformations is decreasing in a neighborhood of its parameter. In addition, we approximate the variance, covariance and correlation between functions of sample means and moments.     

Truncated-exponential skew-symmetric distributions

The family of skew distributions introduced by Azzalini and extended by others has received widespread attention. However, it suffers from complicated inference procedures. In this paper, a new family of skew distributions that overcomes the difficulties is introduced. This new family belongs to the exponential family. Many properties of this family are studied, inference procedures developed and simulation studies performed to assess the procedures. Some particular cases of this family, evidence of its flexibility and a real data application are presented. At least 10 advantages of the new family over Azzalini's distributions are established.