R. K. Saxena and Ravi Saxena
An Extension of the Kratzel Function and Associated Inverse Gaussian Probability Distribution Occurring in Reliability Theory
523 - 532
2009
3
7
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/674
https://publications.waset.org/vol/31
World Academy of Science, Engineering and Technology
In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z FoxWright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gammatype function. Its incomplete forms are also discussed. Several properties of this gammatype function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFoxWright function, Inverse Gaussian distribution, Krtzel function &amp; Bessel function of the third kind.
Open Science Index 31, 2009