In some applied problems we need to choose a population from the given populations and estimate the parameter of the selected population. Suppose k random samples are chosen from k populations with proportional hazard rate model or proportional reversed hazard rate model. According to a specified selection rule, it is desired to estimate the parameter of the best (worst) selected population. In this paper, under the entropy loss function we obtain the uniformly minimum risk unbiased (UMRU) estimator of the parameters of the selected population, and derived sufficient conditions for minimaxity of a given estimator.Then we find the class of admissible and inadmissible linear estimators of the parameters of the selected population and determine the class of dominators of a given estimator. We show that the UMRU estimator is inadmissible and compare the obtained estimators by plotting their risk functions.

Using quantitative models can be a good tool for planning or evaluation. In this regard, given the multifaceted transit (economic, social, political, transportation), estimating the market size and the share of Iran's corridors is the starting point for planning. In this paper, initially, the transit potential is estimated. For prediction, it is applied the gravity model. It is based on examining the trade trends between the economic blocs in the region and beyond. In the next step, implemented the Logit model, for estimating Iran's share of the transit market. The results show that current transit demand is 92 million tones, which is expected to reach 118 million tones based on economic assumptions. Travel time through Iran's corridors without the China-Turkmenistan block is potentially reduced by up to 70%. The likelihood of TurkeyTurkmenistan, India-Ukraine, India-Caucasian economic blocks being attracted to Iran Corridors is 75%, Turkey-India, Turkey-UAE, China-Ukraine, India-Russia 73% and attracting trade between China-Turkmenistan countries and Russia-UAE is estimated at 20%.

Social discount rate is an important variable for the Cost-Benefit analysis. Commonly used discount factor in applied works is exponential discount factor. However, exponential factor has some problems: 1- Determining factors of discount rate and their impacts are varying in time. 2- Empirical and experimental evidences suggest that different individuals and groups of people discount far future with rates lower than early future. 3- If the discount rate were uncertain, it can be shown that the discount rate is decreasing in time. In this paper, we show that the problems can be mitigated by relating the discount rate with hazard rate. That relation can be established using project life probability distribution or its beneficiary’s mortality rate. In this paper, the discount factors of different statistical distribution of projects life are introduced and applied to some countries and Iran. The results show the hazard rate in Iran and India are higher and mean project life are lower than other countries in the sample. 

In this article, according to the importance of the hazard rate function criterion in theevaluation of statistical distributions, its estimation methods are presented. Here, we suggestestimators for the hazard rate function. First, we use the standard deconvolution kerneldensity estimator and suggest a plug-in estimator. In the following we investigate asymptoticbehavior of our estimator. For another estimator, we construct the new estimation thehazard rate function according plug-in and CDF. Finally, we consider the performance ofthe suggested estimators by simulation. Mean square error of estimators λˆ(t, p), λˆ(t) and λˆc(t) present in tables 1 till 6.

The field of ballistic protection assessment is challenging due to the need of satisfying high precision requirements with a limited sample size. Identifying the probability of perforation at a specified projectile velocity is the most common way to quantify the ballistic resistance of a given protection structure. Recently several techniques have been developed for this purpose to assess perforation for all possible velocities. The main drawback of these techniques is the use of the normality assumption under which perforation velocities are expected to follow a Gaussian normal distribution where. Accordingly، any parameter of interest is estimated using the characteristic identified Gaussian distribution. In this work، Interior ballistic data obtained from real tests of intelligence mortar bomb and each selected life distributions applied to the external ballistic data، using the method of maximum likelihood to estimate the model parameters. Then، estimation results from the models compared and evaluated. Different criteria for assessing the goodness of each model investigated. The objective is to identify criteria that can distinguish which life distribution produces the best estimate of the performance of a particular armor model. Another objective of this work is to apply optimal model for obtaining different probabilities، investigating mission reliability، and studying hazard rate behavior of ballistic performance. Lifetime distributions are considered and the Mixture Normal distribution provided optimal results to assess and compare the estimations of ballistic performance data.

Adding parameters to a known distribution is a valuable way of constructing flexible families of distributions. In this paper, we introduce a new model, the modified additive hazard rate model, by replacing the additive hazard rate distribution in the general proportional add ratio model. Next, when two sets of random variables follow the modified additive hazard model, we establish stochastic comparisons between the series and parallel systems comprising these components.