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The ML estimates and fit of the models derived from data set 2

The ML estimates and fit of the models derived from data set 2

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In this research, a new four-parameter lifetime distribution called the Type I Half-Logistic exponentiated Lomax distribution is introduced. The study presents various mathematical properties of this novel model, including moments, moment generating function, quantile function, survival function, and hazard function. Additionally, the behavior of t...

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... The Lomax distribution, characterized by scale and shape parameters, has attracted significant attention due to its utility in modeling real-life datasets across various fields. Numerous researchers have extended the Lomax distribution, as documented in references [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Additionally, many authors [19][20][21][22][23][24][25][26] have utilized the Marshall-Olkin generalized family of distributions because of its applicability in modeling real datasets and its capability to induce skewness into a baseline distribution. ...
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This study introduces the Marshal-Olkin Lomax distribution by compounding the Lomax distribution with the Marshal-Olkin generator. Various statistical properties of this new compound distribution, including the survival function, hazard function, moments, moment generating functions, and order statistics, were derived. The distribution parameters were estimated using the maximum likelihood estimation technique. Subsequently, the newly developed model, along with existing well-known models, was applied to a real-life dataset. The results of this application demonstrated that the newly proposed model outperformed other existing models, as evidenced by the evaluation metrics.
... The Lomax distribution, characterized by scale and shape parameters, has attracted significant attention due to its utility in modeling real-life datasets across various fields. Numerous researchers have extended the Lomax distribution, as documented in references [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Additionally, many authors [19][20][21][22][23][24][25][26] have utilized the Marshall-Olkin generalized family of distributions because of its applicability in modeling real datasets and its capability to induce skewness into a baseline distribution. ...
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Full-text available
This study introduces the Marshal-Olkin Lomax (MOL) distribution by compounding the Lomax distribution with the Marshal-Olkin generator, thereby creating the Marshal-Olkin Lomax (MOL) distribution. Statistical features of the MOL distribution, such as the survival function, hazard function, moments, and moment-generating functions, were derived. The distribution parameters were estimated using the maximum likelihood estimation technique. A simulation study was conducted to assess the consistency of these estimates. The simulation results indicated decreasing bias and RMSE values as sample size increased, demonstrating the distribution's consistency. Subsequently, the newly developed model was compared to existing well-known models by applying it to two real-life datasets. The results of this application demonstrated that the newly proposed model outperformed other existing models, as evidenced by the evaluation metrics. 1. Introduction Contemporary datasets often exhibit complexities such as skewness and kurtosis, posing challenges for fitting them into conventional continuous distributions. In response, researchers have been exploring the development of continuous hybrid distributions to better accommodate these nuances. Unlike normal distributions, which assume a symmetrical bell curve, real-world data often deviate from this ideal, varying in skewness and spread. This necessitates the creation of compound distributions tailored to specific data characteristics. This article delves into the development of such distributions and their application in modeling diverse datasets. One popular method for developing hybrid distributions involves compounding a baseline distribution with a family of distributions, also known as a generator. In this study, we consider the Lomax distribution introduced by [1] as the baseline distribution and the Marshall-Olkin generator developed by [2]. The Lomax distribution, characterized by scale and shape parameters, has attracted significant attention due to its utility in modeling real-life datasets across various fields. Numerous researchers have extended the Lomax distribution, as documented in references [3-18]. Additionally, many authors [19-26] have utilized the Marshall-Olkin generalized family of distributions because of its applicability in modeling real datasets and its capability to induce skewness into a baseline distribution. By compounding the Lomax distribution with the Marshall-Olkin generator, the Marshall-Olkin distribution features constant hazard rates for its marginal distributions, capturing the dependency structure among multiple components effectively. On the other hand, the Lomax distribution has a decreasing hazard rate, suitable for modeling heavy-tailed phenomena where the likelihood of failure decreases over time. By combining these properties, the Marshal-Olkin Lomax distribution aims to offer a flexible hazard rate function that can model the initial high failure rates due to dependencies and the subsequent decrease in failure rates due to heavy tails. Therefore, we aim to create a compound distribution with two shape parameters, enhancing the Lomax distribution's capability to fit datasets exhibiting varying shapes, such as skewness.