The domestication of livestock represented a crucial step in human history. By using endogenous

retroviruses as genetic markers, we found that sheep differentiated on the basis of their “retrotype”

and morphological traits dispersed across Eurasia and Africa via separate migratory episodes.

Relicts of the first migrations include the Mouflon, as well as breeds previously recognized as

“primitive” on the basis of their morphology, such as the Orkney, Soay, and the Nordic short-tailed

A new lifetime class with decreasing failure rateis introduced by compounding truncated Geometric distribution and any proper continuous lifetime distribution. The properties of the proposed class are discussed, including a formal proof of its probability density function, distribution function and explicit algebraic formulae for its reliability and failure rate functions. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented.

In this study a new lifetime class with decreasing failure rate is introduced by compounding truncated logarithmic distribution with any proper continuous lifetime distribution. The properties of the proposed class are discussed, including a formal proof of itsprobability density function, distribution function and explicit algebraic formulae for its reliability and failure rate functions.

A new lifetime class with decreasing failure rate which is obtained by compounding truncated Poisson 
distribution and a lifetime distribution, where the compounding procedure follows same way that was previously 
carried out by Adamidis and Loukas(1998). A general form of probability, distribution, survival and hazard rate 
functions as well as its properties will be presented for such a class. This new class of distributions generalizes 
several distributions which have been introduced and studied in the literature. 

In this paper the researchers are presenting an upper bound for the distribution function of quadratic forms in normal vector with mean zero and positive definite covariance matrix. They also will show that the new upper bound is more precise than the one introduced by Okamoto [4] and the one introduced by Siddiqui [5]. Theoretical Error bounds for both, the new and Okamoto upper bounds are derived in this paper.