Recurrence Relations for Marginal and Joint Moment Generating Functions of Generalized Order Statistics from a New Class of Pareto Distributions

Saran, Jagdish; Nain, Kamal

doi:10.2991/jsta.2016.15.3.6

Cited by 4 publications

(6 citation statements)

References 9 publications

(1 reference statement)

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“…Substituting the above expression for I(x) in (3.6) and simplifying, we derive the relation in (3.5). and 9) we observe that (1.8) reduces to 10) which is the characterizing differential equation for power function distribution with p.d.f. in the form…”

Section: Recurrence Relations For Single Momentsmentioning

confidence: 88%

“…For any result in the initial model of generalized order statistics, there exists a corresponding one in the dual model. Several authors like Ahsanullah (2004), Barakat and El-Adll (2009), Arslan (2010), Jaheen and Al Harbi(2011) and Saran and Pandey (2012) have worked on dgos. Let {X n , n ≥ 1} be a sequence of independent and identically distributed random variables with cdf F(x) and pdf f (x).…”

Section: Introductionmentioning

confidence: 99%

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Recurrence Relations for Single and Product Moments of Dual Generalized Order Statistics from a General Class of Distributions

Saran¹,

Pushkarna²,

Tiwari³

2015

JSTA

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Section: Recurrence Relations For Single Momentsmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Recurrence Relations for Single and Product Moments of Dual Generalized Order Statistics from a General Class of Distributions

Saran¹,

Pushkarna²,

Tiwari³

2015

JSTA

Self Cite

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“…Suppose the random variable Y ∼ TPF with CDF in Equation (2) and PDF in Equation (3) we identify some of the special cases of the TPF distribution as follows. Suppose we define a new random variable X by the transformation:

, then X follows the power function distribution ( Saran and Pandey, 2003 ) which is a special case of the Kumaraswamy distribution ( Kumaraswamy, 1980 ) with CDF

1

and PDF

, for

01

and

0

, then X follows the generalized logistic distribution ( Johnson et al, 1995 ) with CDF

and PDF

, for

and

0

.…”

Section: The New Distributionmentioning

confidence: 99%

“…

, then X follows the power function distribution ( Saran and Pandey, 2003 ) which is a special case of the Kumaraswamy distribution ( Kumaraswamy, 1980 ) with CDF

1

and PDF

, for

01

and

0

.…”

Section: The New Distributionmentioning

confidence: 99%

α-Power transformed transformed power function distribution with applications

Okorie

Ohakwe

Osu

et al. 2021

Heliyon

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By standard transformation of a random variable, we obtained a partially bounded one-parameter version of the bounded three-parameter power function distribution by Saran and Pandey (2004) which we called the Transformed Power Function (TPF) distribution and based on an alpha-power transformation method due to Mahdavi and Kundu (2017) we generalized the TPF distribution as the α -Power Transformed Transformed Power Function ( α PTTPF) distribution. Some of the properties of the α PTTPF distribution are given, and we approached the parameter estimation by three methods, namely: maximum likelihood, ordinary least-squares, and weighted least-squares, but after comparing the results from a simulation study, we settled for the maximum likelihood. The new distribution is suitable for modeling data with either decreasing or upside-down bathtub hazard rates. Three real data-sets are used to demonstrate the usefulness of the new model.

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“…The estimation of the PFD parameters based on record values is studied by Ahsanullah [3]. Saran and Singh [47] developed recurrence relations for the marginal and generating functions of generalized order statistics. Saran and Pandey [46] estimated the parameters of the PFD and proposed a characterization based on kth record values.…”

Section: Introductionmentioning

confidence: 99%

The Weibull-Power Function Distribution With Applications

Tahir¹,

Alizadeh²,

Mansoor³

et al. 2014

HJMS

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Recently, several attempts have been made to define new models that extend well-known distributions and at the same time provide great flexibility in modelling real data. We propose a new four-parameter model named the Weibull-power function (WPF) distribution which exhibits bathtub-shaped hazard rate. Some of its statistical properties are obtained including ordinary and incomplete moments, quantile and generating functions, Rényi and Shannon entropies, reliability and order statistics. The model parameters are estimated by the method of maximum likelihood. A bivariate extension is also proposed. The new distribution can be implemented easily using statistical software packages. We investigate the potential usefulness of the proposed model by means of two real data sets. In fact, the new model provides a better fit to these data than the additive Weibull, modified Weibull, Sarahan-Zaindin modified Weibull and beta-modified Weibull distributions, suggesting that it is a reasonable candidate for modeling survival data.

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Recurrence Relations for Marginal and Joint Moment Generating Functions of Generalized Order Statistics from a New Class of Pareto Distributions

Abstract: In this paper, we establish some recurrence relations for marginal and joint moment generating functions of generalized order statistics from a new class of Pareto distributions. For a particular case these results verify the corresponding results of Athar et al. (2012).

Cited by 4 publications

References 9 publications

Recurrence Relations for Single and Product Moments of Dual Generalized Order Statistics from a General Class of Distributions

Recurrence Relations for Single and Product Moments of Dual Generalized Order Statistics from a General Class of Distributions

α-Power transformed transformed power function distribution with applications

The Weibull-Power Function Distribution With Applications

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