Journal of Statistical Research of Iran
Volume:7 Issue: 2, 2011

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate for the entropy rate of hidden Markov chain by matrix algebra and its spectral representation. To do so, we use the Taylor expansion, and calculate some estimates for the first and the second terms, for the entropy rate of the hidden Markov process and its binary version, respectively. For small є (channel's parameter), the entropy rate has o(є2), as a maximum error, when it is calculated by the first term of Taylor expansion and it has o(є3), as a maximum error, when it is calculated by the second term.

This paper proposes two sampling strategies based on the modified ratio estimator using the population mean of auxiliary variable and population correlation coefficient between the study variable and the auxiliary variable by Singh and Tailor (2003) for estimating the population mean (total) of the study variable in a finite population. A comparative study is made with usual sampling strategies and some concluding remarks are given. Finally, an empirical study is included as an illustration which shows that the proposed sampling strategies are better than Singh and Tailor estimator both in terms of unbiasedness and lesser mean square error.

Ateya and Madhagi (2011) introduced a multivariate form of truncated generalized Cauchy distribution (TGCD), which introduced by Ateya and Al-Hussaini (2007). The multivariate version of (TGCD) is denoted by (MVTGCD). Among the features of this form are that subvectors and conditional subvectors of random vectors, distributed according to this distribution, have the same form of distribution (MVTGCD). They also introduced the joint density function, conditional density function, moment generating function and mixed moments. Also, they estimated all parameters of the distribution using the maximum likelihood and Bayes methods. In this paper, we used the point of view, introduced by Al-Hussaini and Ateya (2010), to obtain the Highest Posterior Density (HPD) prediction intervals of future observations from bivariate truncated generalized Cauchy distribution (BVTGCD).

In contrast to the classical discrete choice experiment, the respondent in a rank-order discrete choice experiment, is asked to rank a number of alternatives instead of the preferred one. In this paper, we study the information matrix of a rank order nested multinomial logit model (RO.NMNL) and introduce local D-optimality criterion, then we obtain Locally D-optimal design for RO.NMNL models in the discrete choice experiment.

This paper considers the problem of estimating the population mean ybar of the study variate y using information on different parameters such as population mean (Xbar), coefficient of variation (Cx), kurtosis (β2(x)), standard deviation (Sx) of the auxiliary variate x and on the correlation coefficient, ρ, between the study variate y and the auxiliary variate x through transformation. A class of estimators on the lines of Kadilar and Cingi (2003) has been defined and its properties are studied to the first degree of approximation. It has been shown that the proposed class of estimators is better than usual unbiased estimator ybar, ratio estimator ybarR, ratio-type estimator tR and Kadilar and Cingi (2003) estimator ybarC under some realistic conditions. Numerical illustration is given in support of the present study.

In this paper, we establish some recurrence relations for single and product moments of generalized order statistics from pth order exponential distribution. Further the results are deduced for the recurrence relations of record values and ordinary order statistics and using a recurrence relation for single moments we obtain characterization of pth order exponential distribution.

This paper deals with a short term forecasting non-stationary time series using wavelets and splines. Wavelets can decompose the series as the sum of two low and high frequency components. Aminghafari and Poggi (2007) proposed to predict high frequency component by wavelets and extrapolate low frequency component by local polynomial fitting. We propose to forecast non-stationary process using splines based on this procedure. This method is applied to forecast simulated data and electricity load consumption of two regions. Result of the study show, the proposed method performance is better than the local polynomial fitting.