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Showing 5 results for Fisher Information
Masoumeh Izanloo, Arezou Habibirad,
Volume 3, Issue 1 (9-2009)
Abstract
Unified hybrid censoring scheme is a mixture of generalized Type-I and Type-II hybrid censoring schemes. In this paper, we mainly consider the analysis of unified hybrid censored data when the lifetime distribution of the individual item is a two-parameter generalized exponential distribution. It is observed that the maximum likelihood estimators can not be obtained in a closed form. We obtain the maximum likelihood estimates of the parameters by using Newton-Raphson algorithm. The Fisher information matrix has been obtained and it can be used for constructing asymptotic confidence intervals. We also obtain the Bayes estimates of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. Simulations are performed to compare the performances of the different schemes and one data set is analyzed for illustrative purposes.
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.
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.
Jafar Ahmadi, Mansoureh Razmkhah,
Volume 11, Issue 1 (9-2017)
Abstract
Consider a repairable system which starts operating at t=0. Once the system fails, it is immediately replaced by another one of the same type or it is repaired and back to its working functions. In this paper, the system's activity is studied from t>0 for a fixed period of time w. Different replacement policies are considered. In each cases, for a fixed period of time w, the probability model and likelihood function of repair process, say window censored, are obtained. The obtained results depend on the lifetime distribution of the original system, so, expression for the maximum likelihood estimator and Fisher information are derived, by assuming the lifetime follows an exponential distribution.
Habib Jafari, Samira Amibigi, Parisa Parsamaram,
Volume 11, Issue 1 (9-2017)
Abstract
Most of the research of design optimality is conducted on linear and generalized linear models. In applicable studies, in agriculture, social sciences, etc, usually in addition to fixed effects, there is also at least one random effect in the model. These models are known as mixed models. In this article, Beta regression model with a random intercept is considered as a mixed model and locally D-optimal design is calculated for simple and quadratic forms of the model and the trend of changes of optimal design points for different parameter values will be studied. For the simple model, a two point locally D-optimal design has been obtained for different parameter values and in the quadratic model, a three point locally D-optimal design has been acquired. Also, according to the efficiency criterion, these locally D-optimal designs are compared with the same designs. It was observed that the efficiency of optimal design, when the random intercept is not considered in the model is lower than the case in which the random effect is considered.
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