1
1726-4057
Iranian Statistical Society
75
60: Probability theory and stochastic processes
Inference for the Proportional Hazards Family under Progressive Type-II Censoring
Asgharzadeh
Akbar
Valiollahi
Reza
1
11
2009
8
1
0
0
09
08
2011
12
09
2015
In this paper, the well-known proportional hazards model which includes several well-known lifetime distributions such as exponential,Pareto, Lomax, Burr type XII, and so on is considered. With both Bayesian and non-Bayesian approaches , we consider the estimation of parameters of interest based on progressively Type-II right censored samples. The Bayes estimates are obtained based on symmetric and asymmetric loss functions. We also provide Bayes and empirical Bayes prediction intervals for the times to failure of units censored in multiple stages in a progressively censored sample. Finally, two numerical examples are given to illustrate the results.
73
60: Probability theory and stochastic processes
Entropy Properties of Certain Record Statistics and Some Characterization Results
Ahmadi
Jafar
1
11
2009
8
1
1
13
09
08
2011
12
09
2015
In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. We prove that sequences of the residual or past entropy of the current records characterizes F in the family of continuous distributions. The exponential and the Frechet distributions are characterized through maximizing Shannon entropies of these statistics under some constraint.
74
60: Probability theory and stochastic processes
Mixed Estimators of Ordered Scale Parameters of Two Gamma Distributions with Arbitrary Known Shape Parameters
Meghnatisi
Zahra
Nematollahi
Nader
1
11
2009
8
1
15
34
09
08
2011
12
09
2015
When an ordering among parameters is known in advance,the problem of estimating the smallest or the largest parametersarises in various practical problems. Suppose independent randomsamples of size ni drawn from two gamma distributions withknown arbitrary shape parameter no_i > 0 and unknown scale parameter beta_i > 0, i = 1, 2. We consider the class of mixed estimators of 1 and 2 under the restriction 0 < beta_1 < beta_2. It has been shown that a subclass of mixed estimators of i, beats the usual estimators frac{bar{X_i}}{nu_i}, i = 1, 2, and a class of admissible estimators in the class of mixed estimators are derived under scale-invariant squared error loss function. Also it has been shown that the mixed estimator of 0<beta_1leq beta_2, (beta_1,beta_2), beats the usual estimator frac{bar{X_1}}{nu_1},frac{bar{X_2}}{nu_2} simultaneously, and a class of admissible estimators in the class of mixed estimators of (beta_1,beta_2) are derived. Finally the results are extended to some subclass of exponential family.
76
60: Probability theory and stochastic processes
Confidence Intervals for the Power of Two-Sided Student’s t-test
Bazargan-Lari
Abdolreza
Jafari
Aliakbar
1
11
2009
8
1
55
60
09
08
2011
12
09
2015
For the power of two-sided hypothesis testing about the mean of a normal population, we derive a 100(1 − alpha)% confidence interval. Then by using a numerical method we will find a shortest confidence interval and consider some special cases.
77
60: Probability theory and stochastic processes
On the Ratio of Rice Random Variables
Bageri Khoolenjani
Nayereh
Khorshidian
Kavous
1
11
2009
8
1
61
71
09
08
2011
12
09
2015
The ratio of independent random variables arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice random variables. Ratios of such random variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) and the existing moments have been derived in terms of several special functions. The delta method is used to approximate moments. As a special case, we have obtained the PDF and CDF of the ratio of independent Rayleigh random variables.