Abstract
In this article, a three-parameter continuous distribution is introduced called Logistic inverse Lomax distribution. We have discussed some mathematical and statistical properties of the distribution such as the probability density function, cumulative distribution function and hazard rate function, survival function, quantile function, the skewness, and kurtosis measures. The model parameters of the proposed distribution are estimated using three well-known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE), and Cramer-Von-Mises estimation (CVME) methods. The goodness of fit of the proposed distribution is also evaluated by fitting it in comparison with some other existing distributions using a real data set.
Highlights
Life-time models are generally used to study the length of the life of components of a system, a device, and in general, reliability and survival analysis
Most of the researchers are attracted towards one parameter logistic distribution for its potential in modeling life-time data, and it has been observed that this distribution has performed excellently in many applications
Applying the similar approach used by (Lan & Leemis, 2008) we have introduced the new distribution called logistic inverse Lomax distribution
Summary
Life-time models are generally used to study the length of the life of components of a system, a device, and in general, reliability and survival analysis. Most of the researchers are attracted towards one parameter logistic distribution for its potential in modeling life-time data, and it has been observed that this distribution has performed excellently in many applications. Joshi et al (2020) has introduced logistic exponential power and its hazard function can exhibit increasing, decreasing, bathtub and upside-down bathtub shaped. Lan and Leemis (2008) has presented an approach to define the logistic compounded model and “The Logistic Inverse Lomax Distribution with Properties and Applications”. Applying the similar approach used by (Lan & Leemis, 2008) we have introduced the new distribution called logistic inverse Lomax distribution. The distribution was defined by Lomax (1954) having a heavy-tailed shaped distribution It can be used in reliability and life testing problems in engineering and in reliability analysis as an alternative distribution (Hassan & Al-Ghamdi, 2009).
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