A New Two-parameter Crack Distribution

Saengthong, Pornpop; Bodhisuwan, Winai

doi:10.3923/jas.2014.758.766

Cited by 3 publications

(2 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This dataset was analyzed by Chananet and Phaphan [26], and the result indicated that the lifetime of the hard drives follow the right skewed distribution. Consequently, five right skewed distributions-twoparameter crack [18], Birnbaum-Saunders [16], inverse Gaussian [17], length-biased inverse Gaussian [17], and the proposed two-sided length-biased inverse Gaussian-are selected for goodness of fit comparison. The parameters of the TS-LBIG distribution are estimated by the suggested estimators.…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…The LBIG distribution has been utilized as a component of mixed distributions. For instance, it was used for constructing a mixture inverse Gaussian distribution [12], new parametrization of mixture inverse Gaussian distribution [13], weighted inverse Gaussian distribution [14], Birnbaum-Saunders distribution [15], re-parametrization of Birnbaum-Saunders distribution [16], three-parameter crack distribution [17], and two-parameter crack distribution [18].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and Applications

Simmachan

Phaphan

2022

Symmetry

View full text Add to dashboard Cite

The notion of length-biased distribution can be used to develop adequate models. Length-biased distribution was known as a special case of weighted distribution. In this work, a new class of length-biased distribution, namely the two-sided length-biased inverse Gaussian distribution (TS-LBIG), was introduced. The physical phenomenon of this scenario was described in a case of cracks developing from two sides. Since the probability density function of the original TS-LBIG distribution cannot be written in a closed-form expression, its generalization form was further introduced. Important properties such as the moment-generating function and survival function cannot be provided. We offered a different approach to solving this problem. Some distributional properties were investigated. The parameters were estimated by the method of the moment. Monte Carlo simulation studies were carried out to appraise the performance of the suggested estimators using bias, variance, and mean square error. An application of a real dataset was presented for illustration. The results showed that the suggested estimators performed better than the original study. The proposed distribution provided a more appropriate model than other candidate distributions for fitting based on Akaike information criterion.

show abstract

Section: Illustrative Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and Applications

Simmachan

Phaphan

2022

Symmetry

View full text Add to dashboard Cite

show abstract

On the Crack Random Numbers Generation Procedure

Ngamkham

2019

Lobachevskii J Math

View full text Add to dashboard Cite

The Performance of Estimators for Generalization of Crack Distribution

Mamuangbon

Budsaba

Volodin

2021

Wseas Transactions on Mathematics

View full text Add to dashboard Cite

In this research, we propose a new four parameter family of distributions called Generalized Crack distribution. We generalizes the family three parameter Crack distribution. The Generalized Crack distribution is a mixture of two parameter Inverse Gaussian distribution, Length-Biased Inverse Gaussian distribution, Twice Length-Biased Inverse Gaussian distribution, and adding one more weight parameter . It is a special case for , where and is the weighted parameter. We investigate the properties of Generalized Crack distribution including first four moments, parameters estimation by using the maximum likelihood estimators and method of moment estimation. Evaluate the performance of the estimators by using bias. The results of simulation are presented in numerically and graphically.

show abstract

A New Two-parameter Crack Distribution

Cited by 3 publications

References 5 publications

Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and Applications

Generalization of Two-Sided Length Biased Inverse Gaussian Distributions and Applications

On the Crack Random Numbers Generation Procedure

The Performance of Estimators for Generalization of Crack Distribution

Contact Info

Product

Resources

About