scholarly journals The Type I Generalized Half-Logistic Distribution Based on Upper Record Values

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Devendra Kumar ◽  
Neetu Jain ◽  
Shivani Gupta
Keyword(s):  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Record Values ◽  
Maximum Likelihood Estimates ◽  
Logistic Distribution ◽  
Type I ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record ◽  
First Four Moments

We consider the type I generalized half-logistic distribution and derive some new explicit expressions and recurrence relations for marginal and joint moment generating functions of upper record values. Here we show the computations for the first four moments and their variances. Next we show that results for record values of this distribution can be derived from our results as special cases. We obtain the characterization result of this distribution on using the recurrence relation for single moment and conditional expectation of upper record values. We obtain the maximum likelihood estimators of upper record values and their confidence intervals. Also, we compute the maximum likelihood estimates of the parameters of upper record values and their confidence intervals. At last, we present one real case data study to emphasize the results of this paper.

scholarly journals Nonparametric Prediction Intervals of generalized order statistics from two independent sequences

2016 ◽  
Vol 4 (1) ◽  
pp. 36 ◽  
Author(s):  
Mostafa Mohie El-Din ◽  
Walid Emam
Keyword(s):  
Order Statistics ◽  
Record Values ◽  
Prediction Intervals ◽  
Generalized Order Statistics ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record ◽  
Nonparametric Prediction ◽  
Nonparametric Prediction Intervals ◽  
Generalized Order

<p>This paper, discusses the problem of predicting future a generalized order statistic of an iid sequence sample was drawn from an arbitrary unknown distribution, based on observed also generalized order statistics from the same population. The coverage probabilities of these prediction intervals are exact and free of the parent distribution F(). Prediction formulas of ordinary order statistics and upper record values are extracted as special cases from the productive results. Finally, numerical computations on several models of ordered random variables are given to illustrate the proposed procedures.</p>

Record-Based Estimators for Weibull Distribution

2014 ◽  
Vol 14 (07) ◽  
pp. 1450026 ◽  
Author(s):  
Mahdi Teimouri ◽  
Saralees Nadarajah
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Likelihood Estimation ◽  
Record Values ◽  
Likelihood Estimator ◽  
Squared Error ◽  
Upper Record Values ◽  
Upper Record

Teimouri and Nadarajah [Statist. Methodol.13 (2013) 12–24] considered bias corrected maximum likelihood estimation of the Weibull distribution based on upper record values. Here, we propose an estimator for the Weibull shape parameter based on consecutive upper records. It is shown by simulations that the proposed estimator has less bias and less mean squared error than an estimator due to Soliman et al. [Comput. Statist. Data Anal.51 (2006) 2065–2077] based on all upper records. Also, the proposed estimator can be considered as a good competitor for the maximum likelihood estimator of the shape parameter based on complete data. This is proved by simulations and using a real dataset.

scholarly journals The Odd Lindley-G Family of Distributions

2017 ◽  
Vol 46 (1) ◽  
pp. 65-87 ◽  
Author(s):  
Frank S. Gomes-Silva ◽  
Ana Percontini ◽  
Edleide de Brito ◽  
Manoel W. Ramos ◽  
Ronaldo Venâncio ◽  
...  
Keyword(s):  
Real Data ◽  
Quantile Function ◽  
Record Values ◽  
Model Parameters ◽  
Baseline Model ◽  
Data Set ◽  
New Family ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record

We propose a new generator of continuous distributions with one extra positive parameter called the odd Lindley-G family. Some special cases are presented. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Various structural properties of the new family, which hold for any baseline model, are derived including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, Renyi entropy, reliability, order statistics and their moments and k upper record values. We discuss estimation of the model parameters by maximum likelihood and provide an application to a real data set.

scholarly journals Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Jung-In Seo ◽  
Jae-Woo Jeon ◽  
Suk-Bok Kang
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Real Data ◽  
Record Values ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Upper Record Values ◽  
Upper Record ◽  
Two Parameter

The maximum likelihood method is the most widely used estimation method. On the other hand, it can produce substantial bias, and an approximate confidence interval based on the maximum likelihood estimator cannot be valid when the sample size is small. Because the sizes of the record values are considerably smaller than the original sequence observed in the majority of cases, a method appropriate for this situation is required for precise inference. This paper provides the exact confidence intervals for unknown parameters and exact predictive intervals for the future upper record values by providing some pivotal quantities in the two-parameter Rayleigh distribution based on the upper record values. Finally, the validity of the proposed inference methods was examined from Monte Carlo simulations and real data.

scholarly journals Maximum likelihood estimation based on type-i hybrid progressive censored competing risks data

2016 ◽  
Vol 4 (1) ◽  
pp. 20
Author(s):  
Samir Ashour ◽  
Wael Abu El Azm
Keyword(s):  
Maximum Likelihood ◽  
Competing Risks ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Data Set ◽  
Special Cases ◽  
Competing Risks Data

<p>This paper is concerned with the estimators problems of the generalized Weibull distribution based on Type-I hybrid progressive censoring scheme (Type-I PHCS) in the presence of competing risks when the cause of failure of each item is known. Maximum likelihood estimates and the corresponding Fisher information matrix are obtained. We generalized Kundu and Joarder [7] results in the case of the exponential distribution while, the corresponding results in the case of the generalized exponential and Weibull distributions may be obtained as a special cases. A real data set is used to illustrate the theoretical results.</p>

scholarly journals Maximum observed likelihood prediction of future record values

Test ◽  
2020 ◽  
Vol 29 (4) ◽  
pp. 1072-1097 ◽  
Author(s):  
Grigoriy Volovskiy ◽  
Udo Kamps
Keyword(s):  
Maximum Likelihood ◽  
Mean Squared Error ◽  
Likelihood Function ◽  
Continuous Distribution ◽  
Record Values ◽  
Extreme Value ◽  
Cumulative Distribution ◽  
Performance Criteria ◽  
Upper Record Values ◽  
Upper Record

AbstractPoint prediction of future upper record values is considered. For an underlying absolutely continuous distribution with strictly increasing cumulative distribution function, the general form of the predictor obtained by maximizing the observed predictive likelihood function is established. The results are illustrated for the exponential, extreme-value and power-function distributions, and the performance of the obtained predictors is compared to that of maximum likelihood predictors on the basis of the mean squared error and the Pitman’s measure of closeness criteria. For exponential and extreme-value distributions, it is shown that under slight restrictions, the maximum observed likelihood predictor outperforms the maximum likelihood predictor in terms of both performance criteria.

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