1
1735-1294
Statistical Research and Training Center - Statistical Centre of Iran
92
General
Taylor Expansion for the Entropy Rate of Hidden Markov Chains
Yar
H.
Nikooravesh
Z.
1
3
2011
7
2
103
120
10
01
2016
10
01
2016
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 chainchr('39')s and channelchr('39')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 varepsilon (channelchr('39')s parameter), the entropy rate has o(varepsilon^2), as a maximum error, when it is calculated by the first term of Taylor expansion and it has o(varepsilon^3) , as a maximum error, when it is calculated by the second term.
88
General
Modified Sampling Strategies Using Correlation Coefficient for Estimating Population Mean
Bhushan
Shashi
Pandey
Arvind
1
3
2011
7
2
121
132
10
01
2016
10
01
2016
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.
87
General
Bayesian Prediction Intervals under Bivariate Truncated Generalized Cauchy Distribution
Ateya
F.
1
3
2011
7
2
133
154
10
01
2016
10
01
2016
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).
89
General
On Rank-Ordered Nested Multinomial Logit Model and D-Optimal Design for this Model
Jafari
Habib
1
3
2011
7
2
155
186
10
01
2016
10
01
2016
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.
91
General
A Study on the Class of Chain Ratioâ€“type Estimators
Singh
P.
Rathour
Anjana
1
3
2011
7
2
187
200
10
01
2016
10
01
2016
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 $(bar{X})$, coefficient of variation $(C_x)$, kurtosis $beta_{2(x)}$, standard deviation $(S_x)$ of the auxiliary variate x and on the correlation coefficient, $rho$, 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 $bar{Y}$, ratio estimator $bar{Y}_R$, ratio-type estimator $t_R$ and Kadilar and Cingi (2003) estimator $bar{Y}_{CR}$ under some realistic conditions. Numerical illustration is given in support of the present study.
90
General
Recurrence Relations for Single and Product Moments of Generalized Order Statistics from pth Order Exponential Distribution and its Characterization
Kumar
Devendra
1
3
2011
7
2
201
212
10
01
2016
10
01
2016
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.
86
General
Using Wavelets and Splines to Forecast Non-Stationary Time Series
Aminghafari
Mina
Roosta
Shokoufeh
1
3
2011
7
2
213
222
10
01
2016
10
01
2016
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.