Existing works on multivariate distributions mainly focus on limited distribution functions and require that the associated marginal distributions belong to the same family. Although this simplifies problems, it may fail to deal with practical cases when the marginal distributions are arbitrary. To this end, copula function is employed since it provides a flexible way in decoupling the marginal...

Trade duration and daily range data often exhibit asymmetric shape with long right tail. In analysing the dynamics of these positively valued time series under autoregressive conditional duration (ACD) models, the choice of the conditional distribution for innovations has posed challenges. A suitably chosen distribution, which is capable of capturing unique characteristics inherent in these dat...

The five parameter gamma–Weibull distribution has been introduced by Leipnik and Pearce (2004). Nadarajah and Kotz (2007) have simplified it into four parameter form, using hypergeometric functions in some special cases. We show that the probability distribution function, all moments of positive order and the characteristic function of gamma–Weibull distribution of a random variable can be expl...

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...

This paper models general survival and the distribution of tumor onset times for various tumors in the data base of control animals developed by the National Toxicology Program. For general survival, a modified Weibull model is shown to give an adequate fit for both Fischer 344 rats and C57BL/6 X C3H F1, mice. In addition, data from control animals in a lifetime study of asbestos are used to su...

Usually, the parameters of a Weibull distribution are estimated by maximum likelihood estimation. To reduce the biases of the maximum likelihood estimators (MLEs) of two-parameter Weibull distributions, we propose analytic bias-corrected MLEs. Two other common estimators of Weibull distributions, least-squares estimators and percentiles estimators, are also introduced. Based on a comparison of ...

in this paper, we develop an inventory model for perishable items with random lifetime in a two-echelon production-distribution system. there is a manufacturer at the first stage that produces its product with a constant rate. deterioration in this stage is modeled via a two-parameter weibull distribution. at the second stage, the retailer places the order and receives the product instantly. th...

By assuming that the underlying distribution belongs to the domain of attraction of an extreme value distribution, one can extrapolate the data to a far tail region so that a rare event can be predicted. However, when the distribution is in the domain of attraction of a Gumbel distribution, the extrapolation is quite limited generally in comparison with a heavy tailed distribution. In view of t...

The Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull distribution, widely used in the reliability context. In this paper, we develop novel GRP models based on probability distributions that stem from the Tsal...

The probabilistic approach has an important place in the wind energy research field as it provides cheap and fast initial information for experts with the help of simulations and estimations. Wind energy experts have been using the Weibull distribution for wind speed data for many years. Nevertheless, there exist cases, where the Weibull distribution is inappropriate with data presenting bimoda...