scholarly journals Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data

2010 ◽  
Vol 2010 ◽  
pp. 1-21
Author(s):  
Z. A. Abo-Eleneen ◽  
E. M. Nigm
Keyword(s):  
Shape Parameter ◽  
Maximum Likelihood Method ◽  
Confidence Region ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Complete Sample ◽  
Generalized Logistic Distribution ◽  
Progressive Type ◽  
Wide Range ◽  
Joint Confidence Region

The reversed generalized logistic (RGL) distributions are very useful classes of densities as they posses a wide range of indices of skewness and kurtosis. This paper considers the estimation problem for the parameters of the RGL distribution based on progressive Type II censoring. The maximum likelihood method for RGL distribution yields equations that have to be solved numerically, even when the complete sample is available. By approximating the likelihood equations, we obtain explicit estimators which are in approximation to the MLEs. Using these approximate estimators as starting values, we obtain the MLEs using iterative method. We examine numerically MLEs estimators and the approximate estimators and show that the approximation provides estimators that are almost as efficient as MLEs. Also we show that the value of the MLEs decreases as the value of the shape parameter increases. An exact confidence interval and an exact joint confidence region for the parameters are constructed. Numerical example is presented in the methods proposed in this paper.

scholarly journals Moment based Estimation for the Shape Parameters, Effect it on Some Probability Statistical Distributions Using the Moment Method and Maximum Likelihood Method

2020 ◽  
Vol 5 (6) ◽  
pp. 979-986
Author(s):  
Hassan Tawakol A. Fadol
Keyword(s):  
Maximum Likelihood ◽  
Shape Parameter ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Estimation Method ◽  
Simulation Method ◽  
Likelihood Method ◽  
Inductive Method ◽  
Binomial Distributions ◽  
Best Estimate

The purpose of this paper was to identify the values of the parameters of the shape of the binomial, bias one and natural distributions. Using the estimation method and maximum likelihood Method, the criterion of differentiation was used to estimate the shape parameter between the probability distributions and to arrive at the best estimate of the parameter of the shape when the sample sizes are small, medium, The problem was to find the best estimate of the characteristics of the society to be estimated so that they are close to the estimated average of the mean error squares and also the effect of the estimation method on estimating the shape parameter of the distributions at the sizes of different samples In the values of the different shape parameter, the descriptive and inductive method was selected in the analysis of the data by generating 1000 random numbers of different sizes using the simulation method through the MATLAB program. A number of results were reached, 10) to estimate the small shape parameter (0.3) for binomial distributions and Poisson and natural and they can use the Poisson distribution because it is the best among the distributions, and to estimate the parameter of figure (0.5), (0.7), (0.9) Because it is better for binomial binomial distributions, when the size of a sample (70) for a teacher estimate The small figure (0.3) of the binomial and boson distributions and natural distributions can be used for normal distribution because it is the best among the distributions.

scholarly journals Alpha Power Transformed Log-Logistic Distribution with Application to Breaking Stress Data

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Maha A. Aldahlan
Keyword(s):  
Maximum Likelihood Method ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Alpha Power ◽  
New Model ◽  
Mathematical Properties

In this paper, a new three-parameter lifetime distribution is introduced; the new model is a generalization of the log-logistic (LL) model, and it is called the alpha power transformed log-logistic (APTLL) distribution. The APTLL distribution is more flexible than some generalizations of log-logistic distribution. We derived some mathematical properties including moments, moment-generating function, quantile function, Rényi entropy, and order statistics of the new model. The model parameters are estimated using maximum likelihood method of estimation. The simulation study is performed to investigate the effectiveness of the estimates. Finally, we used one real-life dataset to show the flexibility of the APTLL distribution.

scholarly journals On the Spike Train Variability Characterized by Variance-to-Mean Power Relationship

2015 ◽  
Vol 27 (7) ◽  
pp. 1530-1548 ◽  
Author(s):  
Shinsuke Koyama
Keyword(s):  
Power Function ◽  
Maximum Likelihood Method ◽  
Brain Regions ◽  
Spike Trains ◽  
Likelihood Method ◽  
Power Relationship ◽  
Mean Power ◽  
Wide Range ◽  
The Mean ◽  
Two Parameters

We propose a statistical method for modeling the non-Poisson variability of spike trains observed in a wide range of brain regions. Central to our approach is the assumption that the variance and the mean of interspike intervals are related by a power function characterized by two parameters: the scale factor and exponent. It is shown that this single assumption allows the variability of spike trains to have an arbitrary scale and various dependencies on the firing rate in the spike count statistics, as well as in the interval statistics, depending on the two parameters of the power function. We also propose a statistical model for spike trains that exhibits the variance-to-mean power relationship. Based on this, a maximum likelihood method is developed for inferring the parameters from rate-modulated spike trains. The proposed method is illustrated on simulated and experimental spike trains.

scholarly journals The Exponentiated Generalized Standardized Half-logistic Distribution

2017 ◽  
Vol 6 (3) ◽  
pp. 24 ◽  
Author(s):  
Gauss M. Cordeiro ◽  
Thiago A. N. De Andrade ◽  
Marcelo Bourguignon ◽  
Frank Gomes-Silva
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Data Set ◽  
Lorenz Curves ◽  
Lifetime Model ◽  
Two Parameter ◽  
New Distribution

We study a new two-parameter lifetime model called the exponentiated generalized standardized half-logistic distribution, which extends the half-logistic pioneered by Balakrishnan in the eighties. We provide explicit expressions for the moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, and order statistics. The model parameters are estimated by the maximum likelihood method. A simulation study reveals that the estimators have desirable properties such as small biases and variances even in moderate sample sizes. We prove empirically that the new distribution provides a better fit to a real data set than other competitive models.

Investigation of Cable Partial Discharge Characteristics Based on Weibull Distribution

2015 ◽  
Vol 737 ◽  
pp. 252-255
Author(s):  
Sheng Hong He ◽  
Qing Hua Zhan ◽  
Yi Ming Zhang ◽  
Yan Ran Li ◽  
Chong Wei ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Shape Parameter ◽  
Maximum Likelihood Method ◽  
Partial Discharge ◽  
Amplitude Distribution ◽  
Likelihood Method ◽  
Defect Model ◽  
Artificial Defect ◽  
Xlpe Cable ◽  
Different Types

In order to study the application of Weibull distribution in cable partial discharge pattern recognition. We apply a 10kV 30m XLPE cable for this study. Then design four kinds of typical artificial defect model and analyze each of defect model’s discharge pulse signals. Finally, estimate the Weibull distribution of signals by use of the maximum likelihood method. The results show that Weibull probability distribution is similar to partial discharge amplitude distribution, the shape parameter β can be used to identify different types of discharge.

Truncated log-logistic Family of Distributions

2020 ◽  
Author(s):  
Mohadese Akbarinasab ◽  
Ali Reza Arabpour ◽  
Abbas Mahdavi
Keyword(s):  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Real Dataset ◽  
New Family ◽  
The Family ◽  
The World ◽  
Family Of Distributions ◽  
Better Than

Background & Aim: There are various data associated with any events in the world which need to be analyzed. In response to this, many researchers attempt to find appropriate methods that could better fit these data using new models. One of these methods is to introduce new distributions which could better describe available data. During last few years, new distributions have been extended based on existing well-known distributions. Usually, new distributions have more parameters than existing ones. This addition of parameter(s) has been proved useful in exploring tail properties and also for improving the goodness-of-fit of the family under study. Methods & Materials: A new family of distributions is introduced by using truncated log-logistic distribution. Some statistical and reliability properties of the new family are derived. Results: Four special lifetime models of the new family are investigated. We estimate the parameters by maximum likelihood method. The obtained results are validated using a real dataset and it is shown that the new distributions provide a better fit than some other known distributions. Conclusion: We have provided four new distributions. The flexibility of the proposed distributions and increased range of skewness was able to fit and capture features in one real dataset much better than some competitor distributions

scholarly journals Parameter Estimation Based on the Frèchet Progressive Type II Censored Data with Binomial Removals

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Mohamed Mubarak
Keyword(s):  
Censored Data ◽  
Time Distribution ◽  
Maximum Likelihood Method ◽  
Failure Time ◽  
Likelihood Method ◽  
Type Ii ◽  
Failure Time Distribution ◽  
Sampling Distributions ◽  
Progressive Type ◽  
Type Ii Censored Data

This paper considers the estimation problem for the Frèchet distribution under progressive Type II censoring with random removals, where the number of units removed at each failure time has a binomial distribution. We use the maximum likelihood method to obtain the estimators of parameters and derive the sampling distributions of the estimators, and we also construct the confidence intervals for the parameters and percentile of the failure time distribution.

scholarly journals Applying Transformer Insulation Using Weibull Extended Distribution Based on Progressive Censoring Scheme

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 100
Author(s):  
Hisham M. Almongy ◽  
Fatma Y. Alshenawy ◽  
Ehab M. Almetwally ◽  
Doaa A. Abdo
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Progressive Type ◽  
Transformer Insulation ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies.

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