scholarly journals Statistical Inference on the Basis of Sequential Order Statistics under a Linear Trend for Conditional Proportional Hazard Rates

2020 ◽  
Vol 8 (2) ◽  
pp. 462-470
Author(s):  
Majid Hashempour ◽  
Mahdi Doostparast ◽  
Zohreh Pakdaman
Keyword(s):  
Fisher Information Matrix ◽  
Linear Trend ◽  
Information Matrix ◽  
Hazard Rates ◽  
Ratio Test ◽  
Proportional Hazard ◽  
Interval Estimates ◽  
Sequential Order Statistics ◽  
Testing Homogeneity ◽  
Component Failures

This paper deals with systems consisting of independent and heterogeneous exponential components. Since failures of components may change lifetimes of surviving components because of load sharing, a linear trend for conditionally proportional hazard rates is considered. Estimates of parameters, both point and interval estimates, are derived on the basis of observed component failures for s(≥ 2) systems. Fisher information matrix of the available data is also obtained which can be used for studying asymptotic behaviour of estimates. The generalized likelihood ratio test is implemented for testing homogeneity of s systems. Illustrative examples are also given.

scholarly journals On Testing Reduction of Left-Censored Weibull Distribution to Exponential Submodel

MENDEL ◽  
2017 ◽  
Vol 23 (1) ◽  
pp. 179-184
Author(s):  
Michal Fusek
Keyword(s):  
Weibull Distribution ◽  
Statistical Model ◽  
Likelihood Ratio Test ◽  
Fisher Information Matrix ◽  
Statistical Tests ◽  
Information Matrix ◽  
Wald Test ◽  
Ratio Test ◽  
Data Modelling ◽  
Power Functions

When analyzing environmental or chemical data, it is often necessary to deal with left-censoredobservations. Since the distribution of the observed variable is often asymmetric, the exponential or the Weibulldistribution can be used. This paper summarizes statistical model of a multiply left-censored Weibull distribution,and estimation of its parameters and their variances using the expected Fisher information matrix. Since inmany situations the Weibull distribution is unnecessarily complicated for data modelling, statistical tests (theLagrange multiplier test, the likelihood ratio test, the Wald test) for assessing suitability of replacement ofthe censored Weibull distribution with the exponential submodel are introduced and their power functions areanalyzed using simulations.

scholarly journals Pareto Type-II Model under Type-I Progressive Hybrid Censoring: Bound Lengths

2020 ◽  
Vol 49 (1) ◽  
pp. 45-59
Author(s):  
Gyan Prakash
Keyword(s):  
Fisher Information Matrix ◽  
Scale Parameter ◽  
Information Matrix ◽  
Real Data ◽  
Type I ◽  
Type Ii ◽  
Data Set ◽  
Interval Estimates ◽  
Bayes Prediction ◽  
Prediction Scenario

The Pareto Type-II model is considered here from which, the observable is to be predicted by using Bayesian approach. The Bayes prediction bound lengths are obtained for Type-I progressive hybrid censored data. Both One-sample and Two-sample Bayes prediction scenario has included in the present study. Both known and unknown cases of the scale parameter have considered in the present study. A comparison also has made with the asymptotic interval estimates, are made-up from the Fisher information matrix. Performance of the different methods has studied by simulation and a real data set.

scholarly journals Optimal design for population pk/pd models

2012 ◽  
Vol 51 (1) ◽  
pp. 115-130
Author(s):  
Sergei Leonov ◽  
Alexander Aliev
Keyword(s):  
Optimal Design ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Optimal Sampling ◽  
Design Algorithm ◽  
Sampling Schemes ◽  
Population Pk ◽  
Different Types

ABSTRACT We provide some details of the implementation of optimal design algorithm in the PkStaMp library which is intended for constructing optimal sampling schemes for pharmacokinetic (PK) and pharmacodynamic (PD) studies. We discuss different types of approximation of individual Fisher information matrix and describe a user-defined option of the library.

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