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Maliheh Abbasnejad Mashhadi, Davood Mohammadi,
Volume 4, Issue 1 (9-2010)
Abstract
In this paper, we characterize symmetric distributions based on Renyi entropy of order statistics in subsamples. A test of symmetry is proposed based on the estimated Renyi entropy. Critical values of the test are computed by Monte Carlo simulation. Also we compute the power of the test under different alternatives and show that it behaves better that the test of Habibi and Arghami (1386).
Abdolreza Sayyareh, Raouf Obeidi,
Volume 4, Issue 1 (9-2010)
Abstract
AIC is commonly used for model selection but the value of AIC has no direct interpretation Cox's test is a generalization of the likelihood ratio test When the true model is unknown based on AIC we select a model but we cannot talk about the closeness of the selected model to the true model Because it is not clear the selected model is wellspecified or mis-specified This paper extends Akaikes AIC-type model selection beside the Cox test for model selection and based on the simulations we study the results of AIC and Cox's test and the ability of these two criterion and test to discriminate models If based on AIC we select a model whether or not Cox's test has a ability of selecting a better model Words which one will considering the foundations of the rival models On the other hand the model selection literature has been generally poor at reflecting the foundations of a set of reasonable models when the true model is unknown As a part of results we will propose an approach to selecting the reasonable set of models
Hamid Reza Chareh, Afshin Fallah,
Volume 4, Issue 2 (3-2011)
Abstract
This paper considers the weight distributions in order to incorporating the topics related to construction of skew-symetric (skew-normal) and bimodal distributions. It discusses that many of skew-normal distributions disscussed in recent years researches can be studid in more general form along with some other interesting aspects in context of weigth distributions. Two cosiderable case of the recent years reaserches have been disscussed. It is shown that the introduced distributions in these reseaches along with all of their interesting properties can be obtain from weigth distribution perspective as only special cases.
Abdolreza Sayyareh,
Volume 4, Issue 2 (3-2011)
Abstract
In this paper we have established for the Kullback-Leibler divergence that the relative error is supperadditive. It shows that a mixture of k rival models gives a better upper bound for Kullback-Leibler divergence to model selection. In fact, it is shown that the mixed model introduce a model which is better than of the all rival models in the mixture or a model which is better than the worst rival model in the mixture.
Ghobad Barmalzan, Abdolreza Sayyareh,
Volume 4, Issue 2 (3-2011)
Abstract
Suppose we have a random sample of size n of a population with true density h(.). In general, h(.) is unknown and we use the model f as an approximation of this density function. We do inference based on f. Clearly, f must be close to the true density h, to reach a valid inference about the population. The suggestion of an absolute model based on a few obsevations, as an approximation or estimation of the true density, h, results a great risk in the model selection. For this reason, we choose k non-nested models and investigate the model which is closer to the true density. In this paper, we investigate this main question in the model selection that how is it possible to gain a collection of appropriate models for the estimation of the true density function h, based on Kullback-Leibler risk.
Shokofeh Zeinodini, Ahmad Parsian,
Volume 4, Issue 2 (3-2011)
Abstract
In this paper, a class of generalized Bayes Minimax estimators of the mean vector of a normal distribution with unknown positive definite covariance matrix is obtained under the sum of squared error loss function. It is shown that this class is an extension of the class obtained by Lin and Tasi (1973).
Behrooz Kavehie, Soghrat Faghihzadeh, Farzad Eskandari, Anooshiravan Kazemnejad, Tooba Ghazanfari,
Volume 4, Issue 2 (3-2011)
Abstract
Sometimes it is impossible to directly measure the effect of intervention (medicine or therapeutic methods) in medical researches. That is because of high costs, long time, the aggressiveness of therapeutic methods, lack of clinical responses, and etc. In such cases, the effect of intervention on surrogate variables is measured. Many statistical studies have been accomplished for measuring the validity of surrogates and introducing a criterion for testing. The first criterion was established based on hypothesis testing. Other criterions were introduced over time. Then by using the classic methods, the Likelihood Ratio Factor was introduced. After that, the Bayesian Likelihood Ratio Factor developed and published. This article aims to introduce the Bayesian Likelihood Ratio Factor based on time dependent data. The illness under study is lung disease in victims of chemical weapons. The surrogate therapy method uses the forced expiratory volume at fist second.
Hamid Esmaili, Mina Towhidi, Seyd Rooalla Roozgar, Mehdi Amiri,
Volume 5, Issue 1 (9-2011)
Abstract
Usually, in testing hypothesis a p_value is used for making decision. Would p_value be the best measure to accept or reject the null hypothesis? Would it be possible to have a better measure than the ordinary p_value? In this paper, hypothesis testing has been considered not as a choice to make decision but as an estimating problem to possible accuracy of a given set, labeled by Θ_0 and p_value would be used as an estimator to possible accuracy of Θ_0 Real numbers as a parametric space has been usually accepted by researcher although the parametric space has been limited in many of applications. A measure named as modified p_value which functions more better than usual p_value in bounded parametric space, would be introduced in normal distribution of one-side and two-side testing.
Eisa Mahmoudi, Reyhaneh Lalehzari,
Volume 5, Issue 1 (9-2011)
Abstract
In this paper a new version of skew uniform distribution is introduced which is completely different from the previous works. Some important properties of the new distribution contain the expression for the density and distribution, kth moments, moment generating and characteristic functions, variance, skewness and kurtusis, mean deviation from the mean, median and mode and parameter estimation are investigated. Also a simulation study on this distribution is carried out to show the consistency of the maximum likelihood and moments estimators. In the end, the new skew uniform distribution is compared with uniform distribution.
Elham Zamanzadeh, Jafar Ahmadi,
Volume 5, Issue 1 (9-2011)
Abstract
In this paper, first a brief introduction of ranked set sampling is presented. Then, construction of confidence intervals for a quantile of the parent distribution based on ordered ranked set sample is given. Because the corresponding confidence coefficient is an step function, one may not be able to find the exact prescribed value. With this in mind, we introduce a new method and show that one can obtained an optimal confidence interval by appealing the proposed approach. We also compare the proposed scheme with the other existence methods.
Ebrahim Konani, Saeid Bagrezaei,
Volume 5, Issue 1 (9-2011)
Abstract
In this article the characterization of distributions is considered by using Kullback-Leibler information and records values. Then some characterizations are obtained based on Kullback-Leibler information and Shannon entropy of order statistics and record values.
Aref Khanjari Idenak, Mohammadreza Zadkarami, Alireza Daneshkhah,
Volume 5, Issue 2 (2-2012)
Abstract
In this paper a new compounding distribution with increasing, decreasing, bathtub shaped and unimodal-bathtub shaped hazard rate function. The new three-parameters distribution as a generalization of the exponential power distribution is proposed. Maximum likelihood estimation of the parameters, raw-moments, density function of the order statistics, survival function, hazard rate function, mean residual lifetime, reliability function and median are presented. Then the properties of this distribution are illustrated based on a real data set.
Mehdi Shams, Mehdi Emadi, Naser Reza Arghami,
Volume 5, Issue 2 (2-2012)
Abstract
In this paper the class of all equivariant is characterized functions. Then two conditions for the proof of the existence of equivariant estimators are introduced. Next the Lehmann's method is generalized for characterization of the class of equivariant location and scale function in terms of a given equivariant function and invariant function to an arbitrary group family. This generalized method has applications in mathematics, but to make it useful in statistics, it is combined with a suitable function to make an equivariant estimator. This of course is usable only for unique transitive groups, but fortunately most statistical examples are of this sort. For other group equivariant estimators are directly obtained.
Khadijeh Mehri, Rahim Chinipardaz,
Volume 5, Issue 2 (2-2012)
Abstract
This article is concerned with the comparison between posterior probability and p-value in two-parameter exponential distribution when the location parameter is considered as extra (nuisance) parameter. It has been shown that for a fixed p-value the posterior probability is increases as the number of observations gets large value. It means that it may be different results between classical and Bayesian point of view. This irreconcilability between classical evidence and Bayesian evidence is remained if we compare the lower bound of posterior probability under a class of reasonable prior distributions.
Zahra Dastmard, Gholamreza Mohtashami Borzadaran, Bagher Moghaddaszadeh Bazaz,
Volume 5, Issue 2 (2-2012)
Abstract
The class of discrete distributions supported on the setup integers is considered. A discrete version of normal distribution can be characterized via maximum entropy. Also, moments, Shannon entropy and Renyi entropy have obtained for discrete symmetric distribution. It is shown that the special cases of this measures imply the discrete normal and discrete Laplace distributions. Then, an analogue of Fisher information is studied by discrete normal, bilateral power series, symmetric discrete and double logarithmic distributions. Also, the conditions under which the above distributions are unimodal are obtained. Finally, central and non-central moments, entropy and maximum entropy of double logarithmic distribution have achieved.
Mohamad Babazadeh, Sadegh Rezaee, Mousa Abdi,
Volume 6, Issue 1 (8-2012)
Abstract
In this paper, a new three-parameter lifetime distribution is introduced by combining an extended exponential distribution with a logarithmic distribution. This flexible distribution has increasing, decreasing and upside-down bathtub failure rate shapes. Various properties of the proposed distribution are discussed. The estimation of the parameters attained by EM algorithm and their asymptotic variance and covariance are obtained. In order to assess the accuracy of the approximation of variance and covariance of the maximum likelihood estimator, a simulation study is presented to illustrate the properties of distribution.
Samaneh Jalambadanis, Mostafa Razmkhah,
Volume 6, Issue 2 (2-2013)
Abstract
In a sequence of multivariate random variables, when the experimenter is interested in ordering one of the variables, the corresponding ordered random variables are referred to as concomitants. In this paper, the distribution properties of the bivariate concomitants of record values and order statistics are first studied. Then, by considering the trivariate pseudo exponential family, the amount of Fisher information contained in these random variables is investigated.
Reza Alizadeh Noughabi, Jafar Ahmadi,
Volume 6, Issue 2 (2-2013)
Abstract
In some practical problems, obtaining observations for the variable of interest is costly and time consuming. In such situations, considering appropriate sampling schemes, in order to reduce the cost and increase the efficiency are worthwhile. In these cases, ranked set sampling is a suitable alternative for simple random sampling. In this paper, the problem of Bayes estimation of the parameter of Pareto distribution under squared error and LINEX loss functions is studied. Using a Monte Carlo simulation, for both sampling methods, namely, simple random sampling and ranked set sampling, the Bayes risk estimators are computed and compared. Finally, the efficiency of the obtained estimators is illustrated throughout using a real data set. The results demonstrate the superiority of the ranked set sampling scheme, therefore, we recommend using ranked set sampling method whenever possible.
Ehsan Zamanzade,
Volume 7, Issue 1 (9-2013)
Abstract
In this paper, two new entropy estimators are proposed. Then, entropy-based tests of exponentiality based on our entropy estimators are introduced. Simulation results show that the proposed estimators and related goodness of fit tests have good performances in comparison with their leading competitors.
Nahid Sanjari Farsipour, Hajar Riyahi,
Volume 7, Issue 2 (3-2014)
Abstract
In this paper the likelihood and Bayesian inference of the stress-strength reliability are considered based on record values from proportional and proportional reversed hazard rate models. Then inference of the stress-strength reliability based on lower record values from some generalized distributions are also considered. Next the likelihood and Bayesian inference of the stress-strength model based on upper record values from Gompertz, Burr type XII, Lomax and Weibull distributions are considered. The ML estimators and their properties are studied. Likelihood-based confidence intervals, exact, as well as the Bayesian credible sets and bootstrap interval for the stress-strength reliability in all distributions are obtained. Simulation studies are conducted to investigate and compare the performance of the intervals.
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