In this paper, we study properties of exp-uniform distribution and its applications. We provide closed forms for the density function and moments of order statistics and we also discuss estimation of the parameters via the maximum likelihood method. We will present certain characterizations of exp-uniform distribution. The applications of this distribution are illustrated by fitting it to three...

We show that for any 1 ≤ t ≤ c̃n log−5/2 n, the set of unconditional convex bodies in R contains a t-separated subset of cardinality at least exp ( exp ( c t2 log(1 + t) n )) . This implies the existence of an unconditional convex body in R which cannot be approximated within the distance d by a projection of a polytope with N faces unless N ≥ exp(c(d)n). We also show that for t ≥ 2, the cardina...

A new family of distributions called the mixture exponentiated Kumaraswamy-G (henceforth, in short, ExpKum-G) class is developed. We consider Weibull distribution as baseline (G) to propose and study this special sub-model, which we call Kumaraswamy distribution. Several useful statistical properties proposed ExpKum-G are derived. Under classical paradigm, maximum likelihood estimation under pr...

The asymptotics of the order of a random permutation have been widely studied. P. Erdös and P. Turán proved that asymptotically the distribution of the logarithm of the order of an element in the symmetric group Sn is normal with mean 12(log n) 2 and variance 13(log n) 3. More recently R. Stong has shown that the mean of the order is asymptotically exp(C √ n/ log n + O( √ n log log n/ log n)) w...

UNLABELLED In this paper, we propose a five-parameter lifetime model called the McDonald exponentiated gamma distribution to extend beta exponentiated gamma, Kumaraswamy exponentiated gamma and exponentiated gamma, among several other models. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the rth moment. We discuss estimation...

Information concentration of probability measures have important implications in learning theory. Recently, it is discovered that the information content of a log-concave distribution concentrates around their differential entropy, albeit with an unpleasant dependence on the ambient dimension. In this work, we prove that if the potentials of the log-concave distribution are exp-concave, which i...

In this paper, the estimation of the unknown parameters of the kumaraswamy distribution is considered using both simple random sampling (SRS) and ranked set sampling (RSS) techniques. The estimation is based on maximum likelihood estimation and Bayesian estimation methods. A simulation study is made to compare the resultant estimators in terms of their biases and mean square errors. The efficie...