Exponential-Poisson distribution: estimation and applications to rainfall and aircraft data with zero occurrence

Louzada, Francisco; Ramos, Pedro Luiz; Ferreira, Paulo H.

doi:10.1080/03610918.2018.1491988

Cited by 20 publications

(9 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The PE distribution has received widespread applications. Among others, the PE distribution has been used to model bowel motility data (Louzada et al 22 ), survival data (Vigas et al 24 ), rainfall data with zero occurrence (Louzada et al 23 ), and aircraft data with zero occurrence (Louzada et al 23 ). Suppose 1 , 2 , … , are independent and identical PE random variables.…”

Section: Model Under Considerationmentioning

confidence: 99%

Reliability analysis of exponentiated Poisson‐exponential constant stress accelerated life test model

Nassar

Dey²,

Nadarajah

2021

Quality & Reliability Eng

View full text Add to dashboard Cite

Accelerated life testing is an efficient tool frequently adopted for obtaining failure time data of test units in a lesser time period as compared to normal use conditions. We assume that the lifetime data of a product at constant level of stress follows an exponentiated Poisson-exponential distribution and the shape parameter of the model has a log-linear relationship with the stress level. Model parameters, the reliability function (RF), and the mean time to failure (MTTF) function under use conditions are estimated based on eight frequentist methods of estimation, namely, method of maximum likelihood, method of least square and weighted least square, method of maximum product of spacing, method of minimum spacing absolute-log distance, method of Cramér-von-Mises, method of Anderson-Darling, and Right-tail Anderson-Darling. The performance of the different estimation methods is evaluated in terms of their mean relative estimate and mean squared error using small and large sample sizes through a Monte Carlo simulation study. Finally, two accelerated life test data sets are considered and bootstrap confidence intervals for the unknown parameters, predicted shape parameter, predicted RF, and the MTTF at different stress levels, are obtained.

show abstract

Section: Model Under Considerationmentioning

confidence: 99%

Reliability analysis of exponentiated Poisson‐exponential constant stress accelerated life test model

Nassar

Dey²,

Nadarajah

2021

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…Lu and Shi (2012) developed and studied the Weibull Poisson distribution. The exponential Poisson was studied by Francisco et al (2020). The exponential Weibull-Poisson distribution which generalises the distribution was derived and studied by Barreto-Souza and Cribari-Neto (2009).…”

Section: Introductionmentioning

confidence: 99%

Lehmann Type II Frechet Poisson Distribution: Properties, Inference and Applications as a Life Time Distribution

Ogunde¹,

Olalude²,

Adeniji³

et al. 2021

IJSP

View full text Add to dashboard Cite

A new generalization of the Frechet distribution called Lehmann Type II Frechet Poisson distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, Renyi entropy, stochastic ordering, Bonferroni and Lorenz curve, mean and median deviation, stress-strength parameter are investigated. The maximum likelihood method is used to estimate the model parameters. We examine the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling three real data sets to illustrate empirically its flexibility and tractability in modeling life time data.

show abstract

“…Other estimation methods that return accurate estimates have been considered, such as estimators based on the least-square function [5], the product of spacing [6,7], or goodness-of-fit statistics [8]. There is not a unique method that performs better in all models, and the performance may depend on the selected parametric form [9,10]. Thus, it is necessary to use an efficient estimation method jointly with a flexible parametric model that covers many data patterns and that sometimes accommodates the asymmetry and multi-modality that may be contained in the data under consideration.…”

Section: Introductionmentioning

confidence: 99%

Generalizing Normality: Different Estimation Methods for Skewed Information

et al. 2021

Self Cite

View full text Add to dashboard Cite

Normality is the most commonly used mathematical supposition in data modeling. Nonetheless, even based on the law of large numbers (LLN), normality is a strong presumption, given that the presence of asymmetry and multi-modality in real-world problems is expected. Thus, a flexible modification in the normal distribution proposed by Elal-Olivero adds a skewness parameter called Alpha-skew-normal (ASN) distribution, which enables bimodality and fat-tail, if needed, although it is sometimes not trivial to estimate this third parameter (regardless of the location and scale). This work analyzed seven different statistical inferential methods towards the ASN distribution on synthetic data and historical data of water flux from 21 rivers (channels) in the Atacama region. Moreover, the contributions of this paper are related to the estimations of probability surrounding rivers’ flux levels in the surroundings of Copiapó city, which is the most economically important city of the third Chilean region and is known to be located in one of the driest areas on Earth (excluding the North and the South Poles). The results show the competitiveness of the MPS and RADE methods with respect to the MLE method, as well as their excellent performance.

show abstract

Exponential-Poisson distribution: estimation and applications to rainfall and aircraft data with zero occurrence

Cited by 20 publications

References 23 publications

Reliability analysis of exponentiated Poisson‐exponential constant stress accelerated life test model

Reliability analysis of exponentiated Poisson‐exponential constant stress accelerated life test model

Lehmann Type II Frechet Poisson Distribution: Properties, Inference and Applications as a Life Time Distribution

Generalizing Normality: Different Estimation Methods for Skewed Information

Contact Info

Product

Resources

About