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.

Logarithm Transformed Lomax Distribution with Applications

2018 ◽  
Vol 70 (2) ◽  
pp. 122-135 ◽  
Author(s):  
Mazen Nassar ◽  
Sanku Dey ◽  
Devendra Kumar
Keyword(s):  
Real Life ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Conditional Moments ◽  
Real Life Data ◽  
Censoring Scheme ◽  
New Distribution

In this article, we introduce a new method for generating distributions which we refer to as logarithm transformed (LT) method. Some statistical properties of the LT method are established. Based on the LT method, we introduce a new generalization of the Lomax distribution that provides better fits than the Lomax distribution and some of its known generalizations. We refer to the new distribution as logarithmic transformed Lomax (LTL) distribution. Various properties of the LTL distribution, including explicit expressions for the moments, quantiles, moment generating function, incomplete moments, conditional moments, Rényi entropy, and order statistics are derived. It appears to be a distribution capable of allowing monotonically decreasing and upside-down bathtub shaped hazard rates depending on its parameters, so it turns out to be quite flexible for analysing non-negative real life data. We discuss the estimation of the model parameters by maximum likelihood method using random censoring scheme. The proposed distribution is utilized to fit a censored data set and the distribution is shown to be more appropriate to the data set than the compared distributions. 2010 Mathematics Subject Classification: 60E05, 60E10, 62E15.

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 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 Some Properties and Applications of Topp Leone Kumaraswamy Lomax Distribution

2021 ◽  
Vol 3 (2) ◽  
pp. 81-94
Author(s):  
Sule Ibrahim ◽  
Sani Ibrahim Doguwa ◽  
Audu Isah ◽  
Haruna, M. Jibril
Keyword(s):  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Data Sets ◽  
Lifetime Distributions ◽  
Air Conditioning System ◽  
Lomax Distribution ◽  
Real Life Data ◽  
New Distribution

Many Statisticians have developed and proposed new distributions by extending the existing distributions. The distributions are extended by adding one or more parameters to the baseline distributions to make it more flexible in fitting different kinds of data. In this study, a new four-parameter lifetime distribution called the Topp Leone Kumaraswamy Lomax distribution was introduced by using a family of distributions which has been proposed in the literature. Some mathematical properties of the distribution such as the moments, moment generating function, quantile function, survival, hazard, reversed hazard and odds functions were presented. The estimation of the parameters by maximum likelihood method was discussed. Three real life data sets representing the failure times of the air conditioning system of an air plane, the remission times (in months) of a random sample of one hundred and twenty-eight (128) bladder cancer patients and Alumina (Al2O3) data were used to show the fit and flexibility of the new distribution over some lifetime distributions in literature. The results showed that the new distribution fits better in the three datasets considered.

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.

scholarly journals Weighted Version of Generalized Inverse Weibull Distribution

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
Sofi Mudasir ◽  
S. P. Ahmad
Keyword(s):  
Weibull Distribution ◽  
Generalized Inverse ◽  
Real Life ◽  
Moment Generating Function ◽  
Weighted Version ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Inverse Weibull Distribution ◽  
Better Than

Weighted distributions are used in many fields, such as medicine, ecology, and reliability. A weighted version of the generalized inverse Weibull distribution, known as weighted generalized inverse Weibull distribution (WGIWD), is proposed. Basic properties including mode, moments, moment generating function, skewness, kurtosis, and Shannon’s entropy are studied. The usefulness of the new model was demonstrated by applying it to a real-life data set. The WGIWD fits better than its submodels, such as length biased generalized inverse Weibull (LGIW), generalized inverse Weibull (GIW), inverse Weibull (IW) and inverse exponential (IE) distributions.

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