Estimation and prediction from gamma distribution based on record values

AL-Dayian, G. R.; Mohammad, Hosny Hassan

doi:10.1016/j.csda.2007.04.002

Cited by 17 publications

(7 citation statements)

References 8 publications

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“…This assumption is not new as considered by many authors like [2,[9][10][11]. The procedure that used in our manuscript (and in the mentioned above papers) is applicable for location-scale family of distributions and the shape parameter (if there is any) is assumed to be known.…”

Section: Discussionmentioning

confidence: 98%

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Record values from NH distribution and associated inference

MirMostafaee

Asgharzadeh

Fallah

2015

METRON

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A new extension of exponential distribution, called NH distribution, was recently introduced by Nadarajah and Haghighi (Statistics 45:543-558, 2011). In this paper, we consider the upper record values from this distribution. We obtain exact explicit expressions as well as several recurrence relations for the single and product moments of record values and then we use these results to compute the means, variances and the covariances of the upper record values. We make use of these calculated moments to find the best linear unbiased estimators (BLUEs) of the location and scale parameters of NH distribution. In addition, based on the observed records, we investigate how to obtain best linear unbiased predictor for the future record values. Confidence intervals for the unknown parameters and prediction intervals for future records are also discussed. Finally, we present an example in order to illustrate the inferential results obtained in this paper and compare the BLUEs with maximum likelihood estimators numerically.

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Section: Discussionmentioning

confidence: 98%

“…The prediction of a future record value is also discussed. Some work in this regard has been done for the normal distribution by [2], for the generalized Pareto distribution by [11], for the generalized exponential distribution by [9] and for the gamma distribution by [10].…”

Section: Introductionmentioning

confidence: 99%

Record values from NH distribution and associated inference

MirMostafaee

Asgharzadeh

Fallah

2015

METRON

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“…Afterward various work on record values have been done including Ahsanullah (1986) rectangular distribution, Ahsanullah and Houchens (1989) Pareto distribution. Ahsanullah (1992) record values of independent and identically distributed continuous random variables, Balakrishnan and Chan (1993) Rayleigh and Weibull distribution, Balakrishnan et al (1995) logistic record values, Ahsanullah and Bhoj (1996) Type-I extreme value distribution, Balakrishnan and Chan (1998) normal records, Sultan et al (2008) gamma distribution based on record values, Teimouri and Gupta (2012) Weibull record values, Sultan (2010) inverse Weibull lifetime model, Shakil and Ahsanullah (2011) ratio of two independently distributed Rayleigh random variables, inverse Gaussian distribution, Bashir, Ahmed and Ahmad (2014) two sided power distribution. Raqab (2000) established the recurrence relations for the moment of record values.…”

Section: Introductionmentioning

confidence: 99%

A Characterization and Recurrence Relations of Moments of the Size-Biased Power Function Distribution by Lower Record Values

Bashir¹,

Rasul²

2018

IJSP

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“…Bayesian estimation and prediction for some life distributions based on record values, including Exponential, Weibull, Pareto and Burr type XII, are discussed in [2]. [21] obtained the best linear unbiased predictors of the next lower records based on observing the first n lower records from gamma distribution. [7] considered prediction of future record values from the exponentiated family of distributions from a Bayesian view point.…”

Section: Introductionmentioning

confidence: 99%

One-sequence and two-sequence prediction for future Weibull records

Bdair¹,

Raqab²

2016

JSTA

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Based on record data, prediction of the future records from the two-parameter Weibull distribution is studied. First we consider the sampling based procedure to compute the Bayes estimates and also to construct symmetric credible intervals. Secondly, we consider one-sequence and two-sequence Bayes prediction of the future records based on some observed records. The Monte Carlo algorithms are used to compute simulation consistent predictors and prediction intervals for future unobserved records. A numerical simulation study is conducted to compare the different methods and a real data set involving the annual rainfall recorded at Los Angeles Civic Center during 132 years is analyzed to illustrate the procedures developed here.

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Estimation and prediction from gamma distribution based on record values

Cited by 17 publications

References 8 publications

Record values from NH distribution and associated inference

Record values from NH distribution and associated inference

A Characterization and Recurrence Relations of Moments of the Size-Biased Power Function Distribution by Lower Record Values

One-sequence and two-sequence prediction for future Weibull records

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