Testing exponentiality based on Laplace transform technique is investigated in last two decades, using this technique we introduce a new test for NBU (2) Class of life distribution. Pitman’s asymptotic efficiencies of this test are calculated and compared with other tests. The percentiles and powers are tabulated for censored and non-censored data. Finally, examples in different areas are used as practical applications of the proposed test.

In this paper point and interval estimations for the three-parameter Burr XII distribution based on joint progressive Type-II censoring scheme are obtained. The maximum likelihood, Bayes and parametric bootstrap methods are used to obtain point estimations for the two distribution parameters. Furthermore, the approximate confidence intervals, four bootstrap confidence intervals and credible intervals of the estimators have been got. The results of Bayes estimators are computed under the squared error loss and linear exponential loss functions using Markov chain Monte Carlo method. Gibbs within Metropolis-Hasting algorithm is applied to generate Markov chain Monte Carlo samples from the posterior density functions. A real data set is used to illustrate the proposed methods. Finally, we carry out a simulation study to compare the performances of the different methods.

Sorting a list of unsorted data is one of the most important problems playing an important rule in many application areas as operations research and computer science. Many sorting algorithms are well-studied but the problem is not to find a way or algorithm to sort elements, but to find an efficient way to sort elements. The output is a stream of data in time. We are interested in this flow of data. For the performance of such algorithms, there has been little research on their stochastic behavior and mathematical properties. In this work we study the mathematical behavior of some different versions sorting algorithms that based on. Using a probabilistic approach, we also discuss the corresponding running time for different strategies like the weighted branching process . Finally we show the existence and the convergence of the related stochastic processes.

The point at issue of this paper is two different treatment methods were used to treat the cystic fibrosis disease for two groups of patients and a statistical tool must be used to compare and investigate the efficacy of the two methods. The stress-strength model is used in a parametric form to compare the efficacy of the two treatment methods. Since, the available data in most clinical situations are censored,the stress-strength model is studied in presence of progressively Type II censored data. The kumaraswamy exponential (Kw-E) distribution is used as a parametric form for the stress-strength model. The statistical inference of the stress-strength reliability R = P[Y < X]is performed when X and Y are independent random variables and follow the Kw-E distribution.

In this work a new class of life distributions, namely used better than aged in moment generating function (UBAmgf) class of life distribution is introduced, Relations of this aging to other well-known aging classes and their applications to a shock model are discussed. Preservations of this aging concept under some reliability operations are also given. Testing exponentiality versus (UBAmgf) class of life distribution is proposed. Pitman's asymptotic efficiencies of the test are calculated and compared with other tests. The percentiles of this test statistic are tabulated.

In this paper, a new test statistic for testing exponentiality against used better than aged in increasing concave ordering UBAC(2) is constructed based on total time on test (TTT)-Transform. Critical values are tabulated for sample size n = 10(5)100. The power of the test is estimated for some commonly used distributions in reliability. Finally, medical applications for real data are proposed to illustrate the theoretical results.