On Birnbaum–Saunders inference

Cysneiros, Audrey H. M. A.; Cribari‐Neto, Francisco; Araújo, Carlos Alberto Gonçalves de

doi:10.1016/j.csda.2008.04.003

Cited by 25 publications

(15 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As showed in Høyland and Rausand (1994, p. 46-48), this follows from the derivation of the BS distribution. As a result, most of the simulation experiments for the BS distribution have been conducted for values of α between 0 and 1; see, for example, Dupuis and Mills (1998), Wu and Wong (2004), Ng et al (2006), Wang et al (2006), Lemonte et al (2007Lemonte et al ( , 2008 and Cysneiros et al (2008). Likewise, we chose values of α in the unit interval to run our simulations and to analyse the simulation findings in detail.…”

Section: Numerical Resultsmentioning

confidence: 99%

Testing hypotheses in the Birnbaum–Saunders distribution under type-II censored samples

Lemonte

Ferrari

2011

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

The two-parameter Birnbaum-Saunders distribution has been used succesfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum-Saunders distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Three empirical applications are presented.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Testing hypotheses in the Birnbaum–Saunders distribution under type-II censored samples

Lemonte

Ferrari

2011

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

show abstract

“…For different inference‐related issues, one may refer to the works of Ahmed et al, Arellano‐Valle et al, Athayde et al, Audrey et al, Azevedo et al, Balakrishnan et al, Balakrishnan and Zhu, Barros et al, Chang and Tang, Cordeiro et al, Cysneiros et al, Desmond and Yang, Farias and Lemonte, Guo et al, Jeng, Lachos et al, Lemonte, Lemonte and Cordeiro, Lemonte et al, Lemonte and Ferrari, Lemonte and Patriota, Li et al, Li and Xu, Lillo et al, Lu and Chang, Meintanis, Moala et al, Niu et al, Padgett and Tomlinson, Pérez and Correa, Qu and Xie, Riquelme et al, Sánchez et al, Santana et al, Santos‐Neto et al, Saulo et al, Sha and Ng, Teimouri et al, Tsionas, Upadhyay and Mukherjee, Vanegas and Paula, Vanegas et al, Vilca et al, Wang, Wang and Fei, Wang et al, Xiao et al, Xie and Wei, Xu and Tang, Xu et al, Zhu and Balakrishnan, and the references cited therein.…”

Section: Concluding Remarks and Further Readingmentioning

confidence: 99%

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

Balakrishnan

Kundu

2018

Appl Stoch Models Bus & Ind

111

View full text Add to dashboard Cite

Birnbaum and Saunders introduced a two-parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix-variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research. KEYWORDSBayes estimators, EM algorithm, Fisher information matrix, hazard function, length-biased distribution, moments and inverse moments, probability density function, stochastic orderings, TP 2 property 4

show abstract

“…where D l = E[D l ] = l is the mean of the demand during the LT (D l ), with defined in (11) and l being the constant and known LT. Here, SS = k q D l is the safety stock (SS), with k q being the SF for a service level q × 100% and D l = √ Var[D l ] = √ l being the standard deviation of the demand during the LT. From (12), note that it is necessary to know the demand distribution during the LT for determining the SF [4]. The SF may be obtained from some percentile of the demand during the LT, which is often the 95th percentile, that is, q = 0.95.…”

Section: Stochastic Inventory Modelsmentioning

confidence: 99%

“…Recently, Vanegas and Paula [9] presented a more general class of distributions including the BS model. Extensive work has been performed on the BS distribution with regard to its properties, inference, methodology, and modeling (e.g., [10][11][12][13][14][15][16][17][18][19]). Although the BS distribution has its genesis from engineering, its applications also include business and industry (e.g., [18,[20][21][22][23][24][25][26][27][28][29]).…”

Section: Introductionmentioning

confidence: 99%

A methodology for stochastic inventory models based on a zero‐adjusted Birnbaum‐Saunders distribution

Leiva

Santos‐Neto

Cysneiros

et al. 2015

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

The Birnbaum-Saunders (BS) distribution is receiving considerable attention. We propose a methodology for inventory logistics that allows demand data with zeros to be modeled by means of a new discrete-continuous mixture distribution, which is constructed by using a probability mass at zero and a continuous component related to the BS distribution. We obtain some properties of the new mixture distribution and conduct a simulation study to evaluate the performance of the estimators of its parameters. The methodology for stochastic inventory models considers also financial indicators. We illustrate the proposed methodology with two real-world demand data sets. It shows its potential, highlighting the convenience of using it by improving the contribution margins of a Chilean food industry.Appl. Stochastic Models Bus. Ind. 2016, 32 74-89 V. LEIVA ET AL.Based on its genesis, the BS distribution considers the duration of a counting period (daily or weekly), which may be switched without collecting extra data, among other properties. It permits the BS distribution to have theoretical arguments for modeling demand data (see details in [30]). Rojas et al. [5] carried out an empirical study in which the BS distribution shows to be a good model to describe the demand for different food products.Despite the wide use of the BS distribution, it is well defined only for positive values. This makes that data sets that contain zero values, such as demand data, cannot be modeled with this distribution. Thus, in the presence of zero values, we should adapt the BS distribution to allow these values to be captured in the modeling. A way for deriving a model suitable to data on the interval [0, ∞) is using a mixture distribution of two components: a BS distribution (continuous component) and a degenerate distribution at a zero value (discrete component). It is well known that the mixture models are powerful and popular tools to generate flexible distributions with good properties [31,32].Santos-Neto et al.[33] proposed a reparameterized BS (RBS) distribution, which has several interesting properties (see also [25,34]). For example, one of the two parameters of the RBS distribution is its mean and the other one a precision parameter. This allows us to make different statistical analyses mimicking the case of the normal distribution, often used to model demand data, but now in an asymmetric framework, which is closer to reality of this kind of data. Then, we use the RBS distribution and a degenerate distribution at zero to construct the demand semi-continuous mixture model. We name this new class of models as the zero-adjusted RBS (ZARBS) distribution, because they are in the line of zero-adjusted models ([35-38]).The main objectives of this paper are as follows: (i) to propose the new ZARBS distribution and (ii) to introduce a methodology for inventory models based on this distribution including financial indicators. We derive several features of the ZARBS distribution and estimate its parameters. We use this distribution because it a...

show abstract

On Birnbaum–Saunders inference

Cited by 25 publications

References 23 publications

Testing hypotheses in the Birnbaum–Saunders distribution under type-II censored samples

Testing hypotheses in the Birnbaum–Saunders distribution under type-II censored samples

Birnbaum‐Saunders distribution: A review of models, analysis, and applications

A methodology for stochastic inventory models based on a zero‐adjusted Birnbaum‐Saunders distribution

Contact Info

Product

Resources

About