Skew-normal alpha-power model

In this paper, authors study properties and inference for the newly introduced skew-normal alpha-power model, generalizing both, the power-normal and skew-normal models. Inference is approached via maximum likelihood. Fisher information matrix is derived and shown to be nonsingular at the whole parametric space. Special emphasis is placed on the special case of the power–skew-normal model. Studies with real data illustrate the fact that the model can be very useful in applications, being able to overfit less general models entertained in the literature.     

Geeta distribution and its properties

A new discrete distribution defined over all the positive integers and with the name of Geeta distribution is described. It is L-shaped like the logarithmic series distribution, Yule distribution and the discrete Pareto distribution but is far more versatile than them as it has two parameters. It belongs to the classes of location parameter distributions, modified power series distributions, Lagrange series distributions and exponential distributions. Its mean fi, variance a2 and two recurrence formulae for higher central moments are obtained. Convolution theorem and variations in the model with changes in the parameters have been considered. ML estimators, MVU estimators and estimators based of mean and variance and on mean and first frequency have been derived.     

Inferences on regression coefficients in a regression model under heteroscedasticity and robustness with respect to departure from normality

In this paper we consider a simple linear regression model under heteroscedasticity and nonnormality. A statistical test for testing the regression coefficient is then derived by assuming normality for the random disturbances and by applying Welch's method. Some Monte Carlo studies are generated for assessing robustness of this test. By combining Tiku's robust procedure with the new test, a robust but more powerful test is developed.     

Computing the probability of hash table/urn overflow

We analyze the probability of a random distribution of n balls into m urns of size b resulting in no overflows. This solves the computational problem associated with a classical combinatorial extreme-value distribution. The problem arose during the analysis of a technique, called perfect hashing, for organizing data in computer files. The results and techniques presented can be used to solve several problems in the analysis of hashing techniques     

Probability density function of quotient of order statistics from the pareto,power and weibull distributions

This paper deals with the probability density functions of quotient of order statistics. We use the Mellin transform technique, to find the distribution of the quotient Z= X/Xwhere X.,X(i < j) are the ith and jth order statistics from the Pareto, Power and Weibull distributions     

Using power transformations when approximating quantiles

Estimators are obtained tor quantiles of survival distributions. This is accomplished by approximating Lritr distribution of the transtorrneri data, where the transformation used is that of Box and Cox (1964). The normal approximation as in Box and Cox and, in addition, the extreme value approximation are considered. More generally, to use the methods given, the approximating distribution must come from a location-scale family. For some commonly used survival random variables T the performance of the above approximations are evaluated in terms of the ratio of the true quantiles of T to the estimated one, in the long run. This performance is also evaluated for lower quantiles using simulated lognormai, Weibull and gamma data. Several examples are given to illustrate the methodology herein, including one with actual data.     

Bayesian multivariate GARCH models with dynamic correlations and asymmetric error distributions

The main goal in this paper is to develop and apply stochastic simulation techniques for GARCH models with multivariate skewed distributions using the Bayesian approach. Both parameter estimation and model comparison are not trivial tasks and several approximate and computationally intensive methods (Markov chain Monte Carlo) will be used to this end. We consider a flexible class of multivariate distributions which can model both skewness and heavy tails. Also, we do not fix tail behaviour when dealing with fat tail distributions but leave it subject to inference.     

Mathematical forms of the distribution of the product of two normal variables

This paper finds the mathematical forms of the distribution of the product where x and x follow a bivariate normal distribution In this paper the distribution when PT0 is expressed as an integral, a new, fundamental result. From this general form, six different cases can be distinguished depending on what is known about the parameters and p. The special cases are Aroian $year:1959 and (6) Additionally, we prove that if and as the distribution of the product approaches the Type III distribution. When p=0# Aroian $year:1959 and Aroian and Meeker $year:1977, give tables for various values of 6., 6 . The results in this paper will be used to provide brief tables for p^O in a separate paper     

Computation of the poisson-inverse gaussian distribution

Recursion relations suitable for rapid computation are derived for the probabilities of the compound Poisson distribution when the compounder is the inverse-Gaussian distribution. Series representation of the probabilities are given. Asymptotic results as well as approximations for probabilities, compared with the exact values, are investigated.