Entropy plays a fundamental role in reliability and system lifetesting areas. In the recent studies, much attentions have been paid to use quantile functions properties and their applications as an alternate approac in distinguishing statistical models and analysis of data. In the present paper, quantile based residual Tsallis entropy is introduced and its properties in continuous models are investigated. Considering distributions of certain lifetime, explicit versions for quantile based residual Tsallis entropy are obtained and their properties monotonicity are studied and characterization based on this entropy is investigated. Also quantile based Tsallis divergence is introduced and quantile based residual Tsallis divergence is obtained. Finally, an estimator for the quantile based residual Tsallis entropy is introduced and its performance is investigate by study simulation.

The aggregate claim amount in a particular time period is a quantity of fundamental importance for proper management of an insurance company and also for pricing of insurance coverages. In this paper, the usual stochastic order between aggregate claim amounts is discussed when the survival function of claims is a increasing and concave. The results established here complete some results of Li and Li (2016).

In this article, we wish to find and select appropriate estimators for statistical population density function using line transect sampling in the present of detection functions with light and heavy tailed distributions. Also it is shown that how the type of detection function could be effective in selection of the best estimator and then we propose a unbiased estimators that has the lower variance than the existed estimators. the simulation results show that if detection functions have heavy tailed distribution, then the new estimators have least mean square error.

Variances homogeneity test are mostly applied as a preliminary test to other analyses like test of equality of means. So far, several tests have been offered in randomized complete block design, that the most prevalent of them are Bartlett and Levene tests, and others are generalized kind of these two tests. The distribution of statistics for these tests are obtained asymptotically. Recently, a test has been introduced base on estimated critical values. In this paper, nine tests are examined based on estimated critical values method and their performance are evaluated with various blocks and treatment groups for normal and t-student distributions by a simulation study. The method of estimated critical values has a good performance in the type I error and a power improvement with respect to using asymptotic distribution.

The complex systems containing of n elements are considered, each having two dependent components. The main goal of this paper is to investigate the mean residual life of such systems with some intact components at time t. Toward this end, the bivariate binomial model and also two different generalizations are described. Finally, some graphical and numerical analyses are provided for mean residual life of such systems under Farlie-Gumbel-Morgenstern model. 

‎Usually in survey sampling when the sensitive questions are asked directly‎, ‎the respondents do not provide true answers‎. ‎The randomized response techniques have been introduced to protect the privacy responses‎. ‎In this article we focus on Simons randomized response technique for qualitative variables‎. ‎Using the combination of the two different‎ ‎Simmons’ models‎, ‎a new combined randomized response technique is introduced to increase protection of privacy‎. ‎Using simulation in R package‎, ‎efficiency of the proposed model is compared to the Simmons’ and Alavi and Tajodini's (1394) models‎. ‎Finally‎, ‎the proposed model has been employed for estimating the proportion of student cheating in Shahid Chamran University‎.

In this paper, a general method for goodness of fit test for the location-scale family of distributions under Type-II progressive censoring is presented and its properties are investigated. Then, using Monte Carlo simulation studies, the power of this test is compared with the powers of some existing tests for testing the Gumbel distribution. Finally the proposed test is used for fitting a distribution to a real data set. 

‎In this paper‎, ‎under certain conditions‎, ‎the usual stochastic‎, ‎convex and dispersive orders between the smallest claim amounts with independent Weibull claims are discussed‎. ‎Also‎, ‎under conditions on some well-known common copula‎, ‎some stochastic comparisons of smallest claim amounts with dependent heterogeneous claims have been obtained‎.

‎Before analyzing a time series data‎, ‎it is better to verify the dependency of the data‎, ‎because if the data be independent‎, ‎the fitting of the time series model is not efficient‎. ‎In recent years‎, ‎the power divergence statistics used for the goodness of fit test‎. ‎In this paper‎, ‎we introduce an independence test of time series via power divergence which depends on the parameter λ‎. ‎We obtain asymptotic distribution of the test statistic‎. ‎Also using a simulation study‎, ‎we estimate the error type I and test power for some λ and n‎. ‎Our simulation study shows that for extremely large sample sizes‎, ‎the estimated error type I converges to the nominal α‎, ‎for any λ‎. ‎Furthermore‎, ‎the modified chi-square‎, ‎modified likelihood ratio‎, ‎and Freeman-Tukey test have the most power‎.

‎The performance of a system depends not only on its design and operation but also on the servicing and maintenance of the item during its operational lifetime‎. ‎Thus‎, ‎the repair and maintenance are important issues in the reliability‎. ‎In this paper‎, ‎a repairable k-out-of-n system is considered that starts operating at time 0‎. ‎If the system fails‎, ‎then it undergoes minimal repair and begins to operate again‎. ‎The reliability function‎, ‎hazard rate function‎, ‎mean residual life function and some reliability properties of the system are obtained by using the connection between the concepts of minimal repair and record values‎. ‎Some known stochastic orders are also used to compare the lifetimes and residual lifetimes of two repairable k-out-of-n systems‎. ‎Finally‎, ‎based on the given information about the lifetimes of k-out-of-n systems‎, ‎some prediction intervals for the lifetime of the proposed repairable system are obtained‎.

‎In many fields such as econometrics‎, ‎psychology‎, ‎social sciences‎, ‎medical sciences‎, ‎engineering‎, ‎etc.‎, ‎we face with multicollinearity among the explanatory variables and the existence of outliers in data‎. ‎In such situations‎, ‎the ordinary least-squares estimator leads to an inaccurate estimate‎. ‎The robust methods are used to handle the outliers‎. ‎Also‎, ‎to overcome multicollinearity ridge estimators are suggested‎. ‎On the other hand‎, ‎when the error terms are heteroscedastic or correlated‎, ‎the generalized least squares method is used‎. ‎In this paper‎, ‎a fast algorithm for computation of the feasible generalized least trimmed squares ridge estimator in a semiparametric regression model is proposed and then‎, ‎the performance of the proposed estimators is examined through a Monte Carlo simulation study and a real data set.

In this study, the E-Bayesian and hierarchical Bayesian for stress-strength, when X and Y are two independent Rayleigh distributions with different parameters were estimated based on the LINEX loss function. These methods were compared with each other and with the Bayesian estimator using Monte Carlo simulation and two real data sets.

‎The parameters of reliability for the most family marginal distribution is estimated with the assumption of independence between two component stress and strength‎, ‎but‎, ‎unfortunately when these two component are correlated‎, ‎have been less discussed‎. ‎Recently‎, ‎a method based on a copula function for estimating the reliability parameter is proposed under the assumption of correlation between stress and strength components‎. ‎In this paper‎, ‎this method is used to estimate the reliability parameter when the distribution of componets is Generalized Exponential (GE)‎. ‎For this purpose FGM‎, ‎generalized FGM and frank copula function have been used‎. ‎Then simulation is also used to demonstrate the suitability of the estimates‎. ‎In the end‎, ‎reliability parameter for data relative contribution of major groups in terms of age breakdown of the population of urban and rural areas in Iran in the year 1390 will be estimated.

In many sample surveys, the variables of interest, such as student cheating in a university are sensitive in nature. In such situations, the interviewees respond to direct questions untruthful, or refuse to answer. The various indirect methods such as randomized response technique and item count technique are introduced to collect sensitive information. In this paper a new item count is proposed, then its randomized version called randomized item count model is introduced. Using this model an unbiased estimator for the sensitive proportion of the population is obtained. The variance of the estimator and an estimate for its variance are obtained. A criterion for comparing efficiency and privacy is introduced simultaneously. Using simulation, the proposed model is evaluated and its efficiency and privacy are compared with the Simons’ technique. Based on this criterion, it is shown that the proposed method is better than the Simons method. The proportion of student cheating in the Shahid Chamran University of Ahvaz is estimated using the proposed model.

‎This paper examines the problem of stochastic‎ ‎comparisons of series and parallel systems with independent and heterogeneous components generalized linear failure rate‎. ‎First‎, ‎we consider two series system with possibly different parameters and obtain the usual stochastic order between the series systems‎. ‎Next‎, ‎we drive the usual stochastic order between parallel systems‎. ‎We also discuss the usual stochastic order between parallel systems by using the unordered majorization and the weighted majorization order between the parameters on the Ɗп.

In this paper, we study a three-parameter bivariate distribution obtained by taking Geometric minimum of Rayleigh distributions. Some important properties of this bivariate distribution have been investigated. It is observed that the maximum likelihood estimators of the parameters cannot be obtained in closed forms. We propose to use the EM algorithm to compute the maximum likelihood estimates of the parameters, and it is computationally quite tractable. Based on an extensive simulated study, the effectiveness of the proposed algorithm is confirmed. We also analyze one real data set for illustrative purposes. Finally, we conclude the paper.

‎We introduce a modified Poisson sampling‎, ‎with a fixed lower bound of sample size‎. ‎The design is‎ ‎a combination of simple random sampling and Poisson sampling‎. ‎Simple random sampling is used to‎ ‎compensate for the lack of sample size from remaining elements in the finite population‎, ‎after execution of a‎

‎Poisson sampling‎. ‎At the first stage‎, ‎the units are sampled independently with given inclusion probabilities‎. ‎But in the‎ ‎second stage‎, ‎inclusion probabilities are dependent to each other‎. ‎Because it is important to know‎, ‎which‎ ‎of the elements are selected in the first stage and which of them are remained‎. ‎Some advantages of our‎ ‎design are‎: ‎simple performance‎, ‎controlling sample size‎, ‎ability to perform the method of probability‎ ‎proportional to size‎. ‎The simulations show that the design can‎ ‎dominate its rival design in probability proportional to size sampling‎.