Abstract
We propose a new generator of continuous distributions with at least four positive parameters called the Kumaraswamy-Odd Rayleigh-G family. Some special cases were presented. The plots of the Kumaraswamy Odd Rayleigh Log-Logistic (KORLL) distribution indicate that the distribution can take many shapes depending on the parameter values. The negative skewness and kurtosis indicates that the distribution has lighter tails than the normal distribution. The Monte Carlo simulation results indicate that the estimated biases decrease when the sample size increases. Furthermore, the root mean squared error estimates decay towards zero as the sample size increases. This part shows the consistency of the maximum likelihood estimators. From the considered analytical measures, the new KORLL provides the best fit to the analysed five real data sets indicating that this new model outclasses its competitors.
Highlights
Researchers use different approaches to induct additional parameters to a continuous class of distributions, ostensibly because in many applications, these classical probability distributions do not fit real life data
We propose a new generator of continuous distributions with at least four positive parameters called the Kumaraswamy-Odd Rayleigh-G family
The Monte Carlo simulation results indicate that the estimated biases decrease when the sample size increases
Summary
Researchers use different approaches to induct additional parameters to a continuous class of distributions, ostensibly because in many applications, these classical probability distributions do not fit real life data. All of these approaches extend the classical baseline probability distributions by introducing additional parameter(s) to the baselines, thereby making the extended baselines much more flexible to fit wide range of data from practical situations. The objective of this paper is to propose a new family of distribution called the Kumaraswamy Odd Rayleigh-G family of distributions which has the capacity of providing more robust compound probability distribution when used in modelling real life data set. This new family adds three additional parameters to the baseline distribution. The Hazard function (hfKORG ) and survival function ( sfKORG ) of the KORG family can be given as hf KORG β
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