Deriving the efficiency function for type I censored sample from Pareto distribution using sup-entropy

2014 ◽  
Vol 33 (2) ◽  
pp. 231-237 ◽  
Author(s):  
Omar A. Kittaneh ◽  
M. Akbar
Keyword(s):  
Pareto Distribution ◽  
Type I ◽  
Efficiency Function ◽  
Censored Sample

On the efficiency of type I censored samples

2021 ◽  
Author(s):  
Omar A Kittaneh ◽  
Heba Almorad, ◽  
Sara Helal ◽  
M A Majid
Keyword(s):  
Probability Distribution ◽  
Simulation Study ◽  
Real Data ◽  
Type I ◽  
Complete Sample ◽  
Efficiency Function ◽  
General Proof ◽  
Censored Samples ◽  
Censored Sample ◽  
Definition Of

Abstract The paper revisits the entropy-based efficiency of the type-I censored sample, which was addressed by several previous works. The main purpose of this work is to provide a comprehensive definition of the efficiency function and give a general proof that the entropy of a censored sample is always less than that of the complete sample for any probability distribution and at any point of censoring. A simulation study is performed to validate our results, and a real-data example is reevaluated.

scholarly journals On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Jin Xia ◽  
Jie Mi ◽  
YanYan Zhou
Keyword(s):  
Maximum Likelihood ◽  
Lognormal Distribution ◽  
Existence And Uniqueness ◽  
Maximum Likelihood Estimators ◽  
Invariance Property ◽  
Type I ◽  
Grouped Data ◽  
Sample Data ◽  
Censored Sample ◽  
Two Parameters

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

scholarly journals Marshall-Olkin Generalized Pareto Distribution: Bayesian and Non Bayesian Estimation

2020 ◽  
pp. 21-33 ◽  
Author(s):  
Hanan Haj AHmad ◽  
Ehab Almetwally
Keyword(s):  
Loss Function ◽  
Bayesian Method ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Model Parameters ◽  
Type I ◽  
Generalized Pareto

A new generalization of generalized Pareto Distribution is obtained using the generator Marshall-Olkin distribution (1997). The new distribution MOGP is more flexible and can be used to model non-monotonic failure rate functions. MOGP includes six different sub models: Generalized Pareto, Exponential, Uniform, Pareto type I, Marshall-Olkin Pareto and Marshall-Olkin exponential distribution. We consider different estimation procedures for estimating the model parameters, namely: Maximum likelihood estimator, Maximum product spacing, Least square method, weighted least square method and Bayesian Method. The Bayesian Method is considered under quadratic loss function and Linex loss function. Simulation analysis using MCMC technique is performed to compare between the proposed point estimation methods. The usefulness of MOGP is illustrated by means of real data set, which shows that this generalization is better fit than Pareto, GP and MOP distributions.

scholarly journals Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 319 ◽  
Author(s):  
Xuehua Hu ◽  
Wenhao Gui
Keyword(s):  
Confidence Intervals ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Delta Method ◽  
Type Ii ◽  
Unknown Parameters ◽  
Hazard Functions ◽  
Generalized Pareto ◽  
Censored Sample ◽  
Type Ii Censored Sample

In this paper, first we consider the maximum likelihood estimators for two unknown parameters, reliability and hazard functions of the generalized Pareto distribution under progressively Type II censored sample. Next, we discuss the asymptotic confidence intervals for two unknown parameters, reliability and hazard functions by using the delta method. Then, based on the bootstrap algorithm, we obtain another two pairs of approximate confidence intervals. Furthermore, by applying the Markov Chain Monte Carlo techniques, we derive the Bayesian estimates of the two unknown parameters, reliability and hazard functions under various balanced loss functions and the corresponding confidence intervals. A simulation study was conducted to compare the performances of the proposed estimators. A real dataset analysis was carried out to illustrate the proposed methods.

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