Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
12
1
2015
9
1
An Extension of the Birnbaum-Saunders Distribution Based on Skew-Normal t Distribution
1
37
EN
Ahad
Jamalizadeh
a.jamalizadeh@uk.ac.ir
Vahid
Amirzadeh
vham51@yahoo.com
Farzaneh
Hashemi
farzane.hashemi1367@yahoo.com
10.18869/acadpub.jsri.12.1.1
In this paper, we introducte a family of univariate Birnbaum-Saunders distributions arising from the skew-normal-t distribution. We obtain several properties of this distribution such as its moments, the maximum likelihood estimation procedure via an EM-algorithm and a method to evaluate standard errors using the EM-algorithm. Finally, we apply these methods to a real data set to demonstrate its flexibility and conduct a simulation study to demonstrate the usefulness of this distribution when compared to the ordinary Birnbaum-Saunders and skew-normal Birnbaum-Saunders distributions.
EM and ECM algorithms, Monte Carlo simulations, observed information matrix, stochastic representation.
http://jsri.srtc.ac.ir/article-1-25-en.html
http://jsri.srtc.ac.ir/article-1-25-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
12
1
2015
9
1
Influence Measures in Ridge Linear Measurement Error Models
39
56
EN
Hadi
Emami
h.emami@znu.ac.ir
10.18869/acadpub.jsri.12.1.39
Usually the existence of influential observations is complicated by the presence of collinearity in linear measurement error models. However no method of influence measure available for the possible effectchr('39')s that collinearity can have on the influence of an observation in such models. In this paper, a new type of ridge estimator based corrected likelihood function (REC) for linear measurement error models is defined. We show when this type of ridge estimator is used to mitigate the effects of collinearity the influence of some observations can be drastically modified. We propose a case deletion formula to detect influential points in REC. As an illustrative example two real data set are analysed.
Corrected likelihood, diagnostics, leverage, measurement error models, shrinkage estimators.
http://jsri.srtc.ac.ir/article-1-23-en.html
http://jsri.srtc.ac.ir/article-1-23-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
12
1
2015
9
1
On the Estimation of Shannon Entropy
57
70
EN
Hadi
Alizadeh Noughabi
alizadehhadi@birjand.ac.ir
10.18869/acadpub.jsri.12.1.57
Shannon entropy is increasingly used in many applications. In this article, an estimator of the entropy of a continuous random variable is proposed. Consistency and scale invariance of variance and mean squared error of the proposed estimator is proved and then comparisons are made with Vasicekchr('39')s (1976), van Es (1992), Ebrahimi et al. (1994) and Correa (1995) entropy estimators. A simulation study is performed and the results indicate that the proposed estimator has smaller mean squared error than competing estimators.
Information theory, entropy estimator, exponential distribution, normal distribution, uniform distribution.
http://jsri.srtc.ac.ir/article-1-22-en.html
http://jsri.srtc.ac.ir/article-1-22-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
12
1
2015
9
1
The Rate of Entropy for Gaussian Processes
71
82
EN
Leila
Golshani
leila_golshani@yahoo.com
10.18869/acadpub.jsri.12.1.71
In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian processes.
Tsallis entropy, Renyi entropy, Shannon entropy, Gaussian process, entropy rate.
http://jsri.srtc.ac.ir/article-1-24-en.html
http://jsri.srtc.ac.ir/article-1-24-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
12
1
2015
9
1
Statistical Inference in Autoregressive Models with Non-negative Residuals
83
104
EN
S.
Zamani Mehryan
s.zamani121@yahoo.com
A.
Sayyareh
asayyareh@kntu.ac.ir
10.18869/acadpub.jsri.12.1.83
Normal residual is one of the usual assumptions of autoregressive models but in practice sometimes we are faced with non-negative residuals case.
In this paper we consider some autoregressive models with non-negative residuals as competing models and we have derived the maximum likelihood estimators of parameters based on the modified approach and EM algorithm for the competing models. Also, based on the simulation study, we have compared the ability of some model selection criteria to select the optimal autoregressive model. Then we consider a set of real data, level of lake Huron 1875-1930, as a data set generated from a first order autoregressive model with non-negative residuals and based on the model selection criteria we select the optimal model between the competing models.
Autoregressive model, Kullback-Leibler information, model selection criterion, modified maximum likelihood.
http://jsri.srtc.ac.ir/article-1-27-en.html
http://jsri.srtc.ac.ir/article-1-27-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
12
1
2015
9
1
Confidence Intervals for Lower Quantiles Based on Two-Sample Scheme
105
116
EN
M.
Razmkhah
razmkha_m@um.ac.ir
H.
Morabbi
H.morabbi@gmail.com
J.
Ahmadi
ahmadi-j@um.ac.ir
10.18869/acadpub.jsri.12.1.105
In this paper, a new two-sampling scheme is proposed to construct appropriate confidence intervals for the lower population quantiles. The confidence intervals are determined in the parametric and nonparametric set up and the optimality problem is discussed in each case. Finally, the proposed procedure is illustrated via a real data set.
Order statistics, coverage probability, optimality, expected width, exponential distribution.
http://jsri.srtc.ac.ir/article-1-26-en.html
http://jsri.srtc.ac.ir/article-1-26-en.pdf