Abstract
In this paper, we introduce a new family of continuous distributions that is called the modified Kies family of distributions. The main mathematical properties of the new family are derived. A special case of the new family has been considered in more detail; namely, the two parameters modified Kies exponential distribution with bathtub shape, decreasing and increasing failure rate function. The importance of the new distribution comes from its ability in modeling positively and negatively skewed real data over some generalized distributions with more than two parameters. The shape behavior of the hazard rate and the mean residual life functions of the modified Kies exponential distribution are discussed. We use the method of maximum likelihood to estimate the distribution parameters based on complete and type-II censored samples. The approximate confidence intervals are also obtained under the two schemes. A simulation study is conducted and two real data sets from the engineering field are analyzed to show the flexibility of the new distribution in modeling real life data.
Highlights
In the last few decades, there have been an increased interest among statisticians to define new families of distributions by adding extra shape parameter to a baseline distribution.The extra parameters of a good generator can usually give lighter tails and heavier tails, accommodate symmetric, unimodal, bimodal, right-skewed and left-skewed density function, and increase and decrease skewness and kurtosis and, more important, yield all types of the hazard function.the extra parameters can provide great flexibility for modelling data in several areas such as economics, engineering, reliability and medical sciences, among others
We propose a new family of distributions based on the modified Kies (MKi) distribution
The main aim of this paper is to introduce and study a new family of distributions which called the modified Kies-G (MKi-G) family
Summary
In the last few decades, there have been an increased interest among statisticians to define new families of distributions by adding extra shape parameter (one or more) to a baseline distribution.The extra parameters of a good generator can usually give lighter tails and heavier tails, accommodate symmetric, unimodal, bimodal, right-skewed and left-skewed density function, and increase and decrease skewness and kurtosis and, more important, yield all types of the hazard function.the extra parameters can provide great flexibility for modelling data in several areas such as economics, engineering, reliability and medical sciences, among others. In the last few decades, there have been an increased interest among statisticians to define new families of distributions by adding extra shape parameter (one or more) to a baseline distribution. The extra parameters of a good generator can usually give lighter tails and heavier tails, accommodate symmetric, unimodal, bimodal, right-skewed and left-skewed density function, and increase and decrease skewness and kurtosis and, more important, yield all types of the hazard function. The extra parameters can provide great flexibility for modelling data in several areas such as economics, engineering, reliability and medical sciences, among others. Proposed the reduced Kies distribution as a special case of the Kies distribution. Mathematics 2020, 8, 1345 the reduced Kies distribution as the modified Kies (MKi) distribution. The cumulative distribution function (CDF) of the MKi distribution is specified (for 0 < t < 1) by
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