Mark Kac introduced a method for calculating the distribution of the integral Av= ∫ T 0 v(Xt) dt for a function v of a Markov process (Xt; t¿0) and a suitable random time T , which yields the Feynman–Kac formula for the moment-generating function of Av. We review Kac’s method, with emphasis on an aspect often overlooked. This is Kac’s formula for moments of Av, which may be stated as follows. F...

he linear exponential distribution is a very well-known distribution for modeling lifetime data in reliability and medical studies.We introduce in this paper a new four-parameter generalized version of the transmuted generalized linear exponential distribution.We provide a comprehensive account of the mathematical properties of the new distributions. In particular, A closed-form expressions for...

A new class of distributions motivated by systems having both series and parallel structures is introduced. Some mathematical properties the (including moment generating function, moments order statistics) are derived. Estimation addressed maximum likelihood method performance estimators assessed a simulation study. An illustration using three failure data sets shows usefulness class.

We introduce and establish some properties of a generalized form of the beta function. Corresponding generalized incomplete beta functions are also defined. Moreover, we define a new probability density function (pdf) involving this new generalized beta function. Some basic functions associated with the pdf, such as moment generating function, mean residue function, and hazard rate function are...

This paper presents an extended lifetime probability distribution based on the alpha power transformation. We refer to proposed as “the Alpha Power Topp-Leone (APTL) distribution”. Mathematical properties of APTL such density and cumulative functions, survival hazard rate quantile function, median, moments its relative measures, weighted moment, moment generating Renyi entropy, order statistics...

In this paper, we propose a new generalization of the Poisson distribution by using concept weighted distribution; trigonometric weight with cosine function is used. We derive some distributional properties distribution, such as cumulative function, moment generating factorial moments, and index dispersion. Then, related model considered for modeling purposes, estimation parameters performed vi...

Take-off is a critical phase of flight, and many birds jump to take the air. Although actuation hindlimb in terrestrial not limited sagittal plane, considerable non-sagittal plane motion has been observed during take-off jumps, how spatial arrangement muscles flying facilitates such jumps received little attention. This study aims ascertain 3D hip muscle function magpie ( Pica pica ), bird know...

In recent decades, there have been numerous endeavors to develop a novel category of survival distributions possessing enhanced flexibility through the extension existing distributions. This article constructs and validates statistical properties distribution in order obtain an alternative that is suitable for analyzing data by presenting mixture Fréchet along with such as probability density f...

We propose an exact method for generating random deviates from continuous order statistics. This versatile method that generates Beta deviates as a middle step can be applied to any density function without resorting to numerical inversion. We also conduct an exhaustive investigation to document the merits of our method in generating deviates from any Beta distribution.

In this article, we investigate the performance of dual-hop amplify-and-forward multiple-input multiple-output relaying system with orthogonal space-time block code transmissions over doubly-correlated Nakagami-m fading channel, where the source, relay, and destination terminals are all equipped with multiple antennas. For two different CSI-assisted relaying schemes, which could be encompassed ...