نشریه اندیشه آماری
سال سیزدهم شماره 2 (پیاپی 26، پاییز و زمستان 1387)

As we mentioned in Part I, we pay attention in this part to the impropriety and inadequacy of the evidential usage of P-value. We, then, discuss an appropriate and legitimate measure, namely the Law of Likelihood, for evidential inference from data.

To select the sample needed for social-economic surveys, it is useful to have a sampling frame. Unfortunately, it happens that one does not have a list containing all units belonging to the target population, but rather another list of units linked in a certain way to the list of target population units. In this case, a sample can be selected from the population with perfect frame in order to produce an estimate for the interested target population by using the links existing between the two populations. If the linkage between the units of two populations is not one-to-one, the problem comes especially from the difficulty to associate a selection probability, or an estimation weight, to the sampled units of the target population. In this paper we describe indirect sampling, record linkage, Generalized Weight Share Method and their application by considering two populations that linked by record linkage method.

In this paper, we consider the estimation problem for the location and scale parameters of the Rayleigh distribution based on doubly type-II censored samples (r initial observations and s final observations are censored). For the Rayleigh distribution, the maximum likelihood method does not provide explicit estimators for the parameters based on type II censored samples. Therefore, we should use some numerical methods for obtaining MLEs. By using Taylor series and approximate likelihood function, we obtain approximate maximum likelihood estimators. Coverage probabilities and confidence intervals for the exact and approximate estimators of scale parameter are derived based on pivotal method and using asymptotic properties of MLEs. By using Monte Carlo simulation for N=10, 30 and r,s=0(1)3, average values of the estimates, their variances and also coverage probabilities and confidence intervals are computed. Finally, we present a numerical example to illustrate the methods of inference developed here.

In complex cases, determination of unknown densities for Bayesian nested models, become possible just by using simulation methods. In this ways, MCMC methods have the most contribution. Solutions of applied examples with various methods of theirs, had given novel ideas to select best methods for examiners. In this paper we remark MCMC methods and attempt by using several of them to solve applied examples by Splus software. Histogram of generation samples from posterior densities is shown.

In this paper, we introduce some methods for testing the common mean vector of several multivariate normal populations with unequal covariance matrices, and compare the power of these tests using the Monte Carlo simulation. At the end, we compare the power of the tests based on an simulated example.

The paradoxes that arise in the calculation of the conditional probabilities are usually the results of the consideration of unsuitable probability space and inattention to the conditional information. In the present paper, some examples that illustrate the general nature of such paradoxes are described.

Markov chains are used in different areas of science for analyzing sequential data. In this note, using the work of Strelioff et. Al. (2007), we show how one can apply Markov chains of various order to finite data to estimate both the parameters and the order of the model through Bayesian methods. Applying methods from information theory, we calculate the relative entropy and the rate of entropy. Finally, by presenting an example, we demonstrate different stages of the finite Markov chain inference.