In a recent article the authors obtained a formula which relates explicitly the tail of risk neutral returns with the wing behavior of the Black Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but a moment generating function is available we first establish, under easy-to-check conditions, tail asymptoics on logarithmic scale as soft applications of st...

Ateya and Madhagi (2011) introduced a multivariate form of truncated generalized Cauchy distribution (TGCD), which introduced by Ateya and Al-Hussaini (2007). The multivariate version of (TGCD) is denoted by (MVTGCD). Among the features of this form are that subvectors and conditional subvectors of random vectors, distributed according to this distribution, have the same form of distribution ...

The inverse Weibull distribution can be readily applied to a wide range of situations including applications in medicine, reliability and ecology. In this article we introduce a new model of generalized inverse Weibull distribution referred to as the Exponentiated generalized inverse distribution. We provide a comprehensive mathematical treatment of this distribution. We derive the moment gener...

A bivariate gamma-type density function involving a confluent hypergeometric function of two variables is being introduced. The inverse Mellin transform technique is employed in conjunction with the transformation of variable technique to obtain its moment generating function, which is expressed in terms of generalized hypergeometric functions. Its cumulative distribution function is given in c...

We introduce a family of statistics, based on the empirical moment generating function, for testing goodness of t to the two-parameter Weibull distribution or, equivalently, to the type I extreme value model. The asymptotic distribution of these statistics correspond to functionals of an appropriate gaussian limiting process. For one of the statistics considered, we estimate, via simulations, s...

 Abstract: A new method to generate various family of distributions is introduced. This method introduces a new two-parameter extension of the exponential distribution to illustrate its application. Some statistical and reliability properties of the new distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean residual lifetime, stochas...

Fractional derivative in time variable is introduced into the Fokker-Planck equation of a population growth model. It’s solution, the KNO scaling function, is transformed into the generating function for the multiplicity distribution. Formulas of the factorial moment and the Hj moment are derived from the generating function, which reduces to that of the negative binomial distribution (NBD), if...

1 Generating Functions 1.1 The ordinary generating function We define the ordinary generating function of a sequence. This is by far the most common type of generating function and the adjective “ordinary” is usually not used. But we will need a different type of generating function below (the exponential generating function) so we have added the adjective “ordinary” for this first type of gene...

In this paper we study the moment generating function order and the new better than used in the moment generating function order (NBUmg) life distributions. A closure property of this order under an independent random sum is deduced, and stochastic comparisons among the block replacement policy, the age replacement policy, the complete repair policy, and the minimal repair policy of an NBUmg co...