1
1726-4057
Iranian Statistical Society
67
60: Probability theory and stochastic processes
A Bayesian Approach to Estimate Parameters of a Random Coefficient Transition Binary Logistic Model with Non-monotone Missing Pattern and some Sensitivity Analyses
Eftekhari Mahabadi
Samaneh
Ganjali
Mojtaba
1
11
2010
9
2
1
21
06
08
2011
12
09
2015
A transition binary logistic model with random coefficients is proposed to
model the unemployment statues of household members in two seasons of spring
and summer. Data correspond to the labor force survey performed by
Statistical Center of Iran in 2006. This model is introduced to take into
account two kinds of correlation in the data one due to the longitudinal
nature of the study, that will be considered using a transition model,
and the other due to the assumed correlation between responses of members
of the same household which is taken into account byintroducing random
coefficients into the model. Due to the use of special sampling method in
this survey (rotation sampling), some kinds of non-monotone missing pattern
occur that are considered in the proposed model using the breakdown of the
joint distribution of the response variables. A Bayesian approach is used
to estimate model parameters via the Gibbs sampling method and data
augmentation. Results of using this model are compared with those of three
other transitional models. The most applicable model which gains more
interpretability and precision due to consideration of all aspects of the
collected data is found. Also some sensitivity analysis are performed to
assess asymmetric departures from the logistic link function and robustness
of the posterior estimation of the transition parameter to the perturbations
of the prior parameters.
68
60: Probability theory and stochastic processes
ADK Entropy and ADK Entropy Rate in Irreducible- Aperiodic Markov Chain and Gaussian Processes
Khodabin
Morteza
1
11
2010
9
2
115
126
06
08
2011
12
09
2015
In this paper, the two parameter ADK entropy, as a generalized of Re'nyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this entropy is discussed. The ADK entropy rate is dened and is used for deriving the entropy rate of stationary Gaussian processes and an irreducible- aperiodic Markov chain.
69
60: Probability theory and stochastic processes
Point Prediction for the Proportional Hazards Family under Progressive Type-II Censoring
Asgharzadeh
Akbar
Valiollahi
Reza
1
11
2010
9
2
127
148
06
08
2011
12
09
2015
In this paper, we discuss dierent predictors of times to failure of units censored in multiple stages in a progressively censored sample from proportional hazard rate models. The maximum likelihood predictors, best unbiased predictors and conditional median predictors are considered. We also consider Bayesian point predictors for the times to failure of units. A numerical example and a Monte Carlo simulation study are presented to illustrate all the prediction methods discussed in this paper.
71
60: Probability theory and stochastic processes
On Estimation Following Selection with Applications on k-Records and Censored Data
Naghizadeh Qomi
Mehran
Nematollahi
Nader
Parsian
Ahmad
1
11
2010
9
2
149
169
06
08
2011
12
09
2015
Let X1 and X2 be two independent random variables from gamma populations Pi1,P2 with means alphaθ1 and alphaθ2 respectively, where alpha(> 0) is the common known shape parameter and θ1 and θ2 are scale parameters. Let X(1) ≤ X(2) denote the order statistics ofX1 and X2. Suppose that the population corresponding to the largest X(2) (or the smallest X(1)) observation is selected. The problem ofinterest is to estimate the scale parameters θM (and θJ ) of the selected gamma population under an asymmetric scale invariant loss function.We characterize admissible estimators of θM (or θJ ) within the class of linear estimators of the form cX(2) (or cX(1)). In estimating θM,we derive a minimax estimator and provide sufficient conditions for the inadmissibility of arbitrary invariant estimators of θM. We apply our results to k-Records and censored data. Finally, we extend our results to a subclass of exponential family of distributions.
72
60: Probability theory and stochastic processes
Estimation of Parameters for an Extended Generalized Half Logistic Distribution Based on Complete and Censored Data
Torabi
Hamzeh
Bagheri
Fatemeh
1
11
2010
9
2
171
195
06
08
2011
12
09
2015
This paper considers an Extended Generalized Half Logistic distribution. We derive some properties of this distribution and then we discuss estimation of the distribution parameters by the methods of moments, maximum likelihood and the new method of minimum spacing distance estimator based on complete data. Also, maximum likelihood equations for estimating the parameters based on Type-I and Type-II censored data are given. In addition, the asymptotic variance and covariance of the estimators are given. We then evaluate the properties of maximum likelihood estimation (MLE) through the mean squared error, relative absolute bias and relative error. Furthermore, the asymptotic con¯dence intervals of the estimators are presented. Finally, simulation results are carried out to study the precision of the MLEs for the parameters involved.