scholarly journals A New Extended Model with Bathtub-Shaped Failure Rate: Properties, Inference, Simulation and Applications

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2024
Author(s):  
Alya Al Al Mutairi ◽  
Muhammad Z. Iqbal ◽  
Muhammad Z. Arshad ◽  
Badr Alnssyan ◽  
Hazem Al-Mofleh ◽  
...  
Keyword(s):  
Applied Sciences ◽  
Real Life ◽  
Parametric Models ◽  
Model Parameters ◽  
Extended Model ◽  
Censored Samples ◽  
Real Life Data ◽  
Rate Functions ◽  
Competing Models ◽  
Likelihood Approach

Theoretical and applied researchers have been frequently interested in proposing alternative skewed and symmetric lifetime parametric models that provide greater flexibility in modeling real-life data in several applied sciences. To fill this gap, we introduce a three-parameter bounded lifetime model called the exponentiated new power function (E-NPF) distribution. Some of its mathematical and reliability features are discussed. Furthermore, many possible shapes over certain choices of the model parameters are presented to understand the behavior of the density and hazard rate functions. For the estimation of the model parameters, we utilize eight classical approaches of estimation and provide a simulation study to assess and explore the asymptotic behaviors of these estimators. The maximum likelihood approach is used to estimate the E-NPF parameters under the type II censored samples. The efficiency of the E-NPF distribution is evaluated by modeling three lifetime datasets, showing that the E-NPF distribution gives a better fit over its competing models such as the Kumaraswamy-PF, Weibull-PF, generalized-PF, Kumaraswamy, and beta distributions.

scholarly journals Weighted Power Lomax Distribution and its Length Biased Version: Properties and Estimation Based on Censored Samples

2021 ◽  
pp. 343-356
Author(s):  
Amal Soliman Hassan ◽  
Ehab M. Almetwally ◽  
Mundher Abdullah Khaleel ◽  
Heba Fathy Nagy
Keyword(s):  
Real Life ◽  
Model Parameters ◽  
Weighted Version ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Lifetime Distributions ◽  
Lomax Distribution ◽  
Censored Samples ◽  
Real Life Data ◽  
Asymptotic Confidence Intervals

In this paper, a weighted version of the power Lomax distribution referred to the weighted power Lomax distribution, is introduced. The new distribution comprises the length biased and the area biased of the power Lomax distribution as new models as well as containing an existing model as the length biased Lomax distribution as special model. Essential distributional properties of the weighted power Lomax distribution are studied. Maximum likelihood and maximum product spacing methods are proposed for estimating the population parameters in cases of complete and Type-II censored samples. Asymptotic confidence intervals of the model parameters are obtained. A sample generation algorithm along with a Monte Carlo simulation study is provided to demonstrate the pattern of the estimates for different sample sizes. Finally, a real-life data set is analyzed as an illustration and its length biased distribution is compared with some other lifetime distributions.

scholarly journals Marshall-Olkin Power Lomax Distribution: Properties and Estimation Based on Complete and Censored Samples

2019 ◽  
Vol 9 (1) ◽  
pp. 48 ◽  
Author(s):  
Muhammad Ahsan Ul Haq ◽  
G. G. Hamedani ◽  
M. Elgarhy ◽  
Pedro Luiz Ramos
Keyword(s):  
Mean Squared Error ◽  
Real Life ◽  
Moment Generating Function ◽  
Model Parameters ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Lomax Distribution ◽  
Censored Samples ◽  
Real Life Data ◽  
Proposed Model

We study a new distribution called the Marshall-Olkin Power Lomax distribution. A comprehensive account of its mathematical properties including explicit expressions for the ordinary moments, moment generating function, order statistics, Renyi entropy, and probability weighted moments are derived. The model parameters are estimated by the method of maximum likelihood. Monte Carlo simulation study is carried out to estimate the parameters and the performance of the estimates is judged via the average biases and mean squared error values. The usefulness of the proposed model is illustrated via real-life data set.

scholarly journals Bayesian and Classical Inference under Type-II Censored Samples of the Extended Inverse Gompertz Distribution with Engineering Applications

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1578
Author(s):  
Ahmed Elshahhat ◽  
Hassan M. Aljohani ◽  
Ahmed Z. Afify
Keyword(s):  
Real Life ◽  
Rate Function ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Alpha Power ◽  
Type Ii ◽  
Failure Rate Function ◽  
Censored Samples ◽  
Inverse Gamma ◽  
Bathtub Shape

In this article, we introduce a new three-parameter distribution called the extended inverse-Gompertz (EIGo) distribution. The implementation of three parameters provides a good reconstruction for some applications. The EIGo distribution can be seen as an extension of the inverted exponential, inverse Gompertz, and generalized inverted exponential distributions. Its failure rate function has an upside-down bathtub shape. Various statistical and reliability properties of the EIGo distribution are discussed. The model parameters are estimated by the maximum-likelihood and Bayesian methods under Type-II censored samples, where the parameters are explained using gamma priors. The performance of the proposed approaches is examined using simulation results. Finally, two real-life engineering data sets are analyzed to illustrate the applicability of the EIGo distribution, showing that it provides better fits than competing inverted models such as inverse-Gompertz, inverse-Weibull, inverse-gamma, generalized inverse-Weibull, exponentiated inverted-Weibull, generalized inverted half-logistic, inverted-Kumaraswamy, inverted Nadarajah–Haghighi, and alpha-power inverse-Weibull distributions.

Combining Non-Parametric and Parametric Models for Stable and Computationally Efficient Battery Health Estimation

2020 ◽  
Author(s):  
Antti Aitio ◽  
David Howey
Keyword(s):  
Latent Variables ◽  
Linear Time ◽  
Full Range ◽  
Real Life ◽  
Internal Resistance ◽  
State Of Charge ◽  
Parametric Models ◽  
Model Parameters ◽  
Battery Management ◽  
Resistance Change

Abstract Equivalent circuit models for batteries are commonly used in electric vehicle battery management systems to estimate state of charge and other important latent variables. They are computationally inexpensive, but suffer from a loss of accuracy over the full range of conditions that may be experienced in real-life. One reason for this is that the model parameters, such as internal resistance, change over the lifetime of the battery due to degradation. However, estimating long term changes is challenging, because parameters also change with state of charge and other variables. To address this, we modelled the internal resistance parameter as a function of state of charge and degradation using a Gaussian process (GP). This was performed computationally efficiently using an algorithm [1] that interprets a GP to be the solution of a linear time-invariant stochastic differential equation. As a result, inference of the posterior distribution of the GP scales as 𝒪(n) and can be implemented recursively using a Kalman filter.

A new generalized version of Log-logistic distribution with applications in medical sciences and other applied fields

2018 ◽  
Vol 09 (05) ◽  
pp. 1850043
Author(s):  
Bilal Ahmad Para ◽  
Tariq Rashid Jan
Keyword(s):  
Real Life ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Medical Sciences ◽  
Real Life Data ◽  
Proposed Model ◽  
Asymptotic Confidence Intervals ◽  
Mc Simulation ◽  
Robust Measures ◽  
Applied Fields

In this paper, we studied a two-parameter transmuted model of Log-logistic distribution (LLD) using the quadratic rank transmutation map technique studied by Shaw and Buckley1 as a new survival model in medical sciences and other applied fields. Statistical properties of Transmuted LLD (TLLD) are discussed comprehensively. Robust measures of skewness and kurtosis of the proposed model have also been discussed along with graphical overview. The estimation of the model parameters is performed by Maximum Likelihood (ML) method followed by a Monte Carlo (MC) simulation procedure to investigate the performance of the ML estimators and the asymptotic confidence intervals of the parameters. Applications of the proposed model to real-life data are also presented.

scholarly journals Properties, Inference and Applications of Alpha Power Extended Inverted Weibull Distribution

2020 ◽  
Vol 9 (6) ◽  
pp. 90
Author(s):  
A. A. Ogunde ◽  
S. T. Fayose ◽  
B. Ajayi ◽  
D. O. Omosigho
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Real Life ◽  
Simulation Method ◽  
Quantile Function ◽  
Transformation Method ◽  
Model Parameters ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data

In this work, we introduce a new generalization of the Inverted Weibull distribution called the alpha power Extended Inverted Weibull distribution using the alpha power transformation method. This approach adds an extra parameter to the baseline distribution. The statistical properties of this distribution including the mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and moment generating functions, reliability analysis, Lorenz and Bonferroni and curves, Rényi of entropy and order statistics are studied. We consider the method of maximum likelihood for estimating the model parameters and the observed information matrix is derived. Simulation method and three real life data sets are presented to demonstrate the effectiveness of the new model.

scholarly journals Some New Contributions on the Marshall–Olkin Length Biased Lomax Distribution: Theory, Modelling and Data Analysis

2020 ◽  
Vol 25 (4) ◽  
pp. 79 ◽  
Author(s):  
Jismi Mathew ◽  
Christophe Chesneau
Keyword(s):  
Real Life ◽  
Stochastic Ordering ◽  
Strength Parameter ◽  
Data Sets ◽  
Lifetime Distributions ◽  
Lomax Distribution ◽  
Real Life Data ◽  
Likelihood Approach ◽  
Useful Lifetime

The Lomax distribution is arguably one of the most useful lifetime distributions, explaining the developments of its extensions or generalizations through various schemes. The Marshall–Olkin length-biased Lomax distribution is one of these extensions. The associated model has been used in the frameworks of data fitting and reliability tests with success. However, the theory behind this distribution is non-existent and the results obtained on the fit of data were sufficiently encouraging to warrant further exploration, with broader comparisons with existing models. This study contributes in these directions. Our theoretical contributions on the the Marshall–Olkin length-biased Lomax distribution include an original compounding property, various stochastic ordering results, equivalences of the main functions at the boundaries, a new quantile analysis, the expressions of the incomplete moments under the form of a series expansion and the determination of the stress–strength parameter in a particular case. Subsequently, we contribute to the applicability of the Marshall–Olkin length-biased Lomax model. When combined with the maximum likelihood approach, the model is very effective. We confirm this claim through a complete simulation study. Then, four selected real life data sets were analyzed to illustrate the importance and flexibility of the model. Especially, based on well-established standard statistical criteria, we show that it outperforms six strong competitors, including some extended Lomax models, when applied to these data sets. To our knowledge, such comprehensive applied work has never been carried out for this model.

scholarly journals On a modified Burr XII distribution having flexible hazard rate shapes

2020 ◽  
Vol 70 (1) ◽  
pp. 193-212
Author(s):  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
M. Arslan Nasir ◽  
Abdus Saboor ◽  
Emrah Altun ◽  
...  
Keyword(s):  
Hazard Rate ◽  
Real Life ◽  
Stochastic Ordering ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Burr Xii Distribution ◽  
Life Data ◽  
Real Life Data

AbstractIn this paper, we propose a new three-parameter modified Burr XII distribution based on the standard Burr XII distribution and the composition technique developed by [14]. Among others, we show that this technique has the ability to significantly increase the flexibility of the former Burr XII distribution, with respect to the density and hazard rate shapes. Also, complementary theoretical aspects are studied as shapes, asymptotes, quantiles, useful expansion, moments, skewness, kurtosis, incomplete moments, moments generating function, stochastic ordering, reliability parameter and order statistics. Then, a Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates of the modified Burr XII model parameters. Finally, three applications to real-life data sets are presented, with models comparisons. The results are favorable for the new modified Burr XII model.

scholarly journals A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Pelumi E. Oguntunde ◽  
Mundher A. Khaleel ◽  
Mohammed T. Ahmed ◽  
Adebowale O. Adejumo ◽  
Oluwole A. Odetunmibi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Real Life ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Lomax Distribution ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Better Than

Developing new compound distributions which are more flexible than the existing distributions have become the new trend in distribution theory. In this present study, the Lomax distribution was extended using the Gompertz family of distribution, its resulting densities and statistical properties were carefully derived, and the method of maximum likelihood estimation was proposed in estimating the model parameters. A simulation study to assess the performance of the parameters of Gompertz Lomax distribution was provided and an application to real life data was provided to assess the potentials of the newly derived distribution. Excerpt from the analysis indicates that the Gompertz Lomax distribution performed better than the Beta Lomax distribution, Weibull Lomax distribution, and Kumaraswamy Lomax distribution.

scholarly journals A New Extended Burr XII Distribution

2017 ◽  
Vol 46 (1) ◽  
pp. 33-39 ◽  
Author(s):  
Indranil Ghosh ◽  
Marcelo Bourguinon
Keyword(s):  
Real Life ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Burr Xii Distribution ◽  
Life Data ◽  
Real Life Data ◽  
Proposed Model ◽  
New Distribution

In this paper, we propose a new lifetime distribution, namely the extended Burr XII distribution (using the technique as mentioned in Cordeiro et al. (2015)). We derive some basic properties of the new distribution and provide a Monte Carlo simulation study to evaluate the maximum likelihood estimates of model parameters. For illustrative purposes, two real life data sets have been considered as an application of the proposed model.

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