A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications

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.

The Odd Weibull Inverse Topp–Leone Distribution with Applications to COVID-19 Data

“…This section is dedicated to demonstrate the potential of two real data sets for the OWITL distribution. Compared with other competitive models, OWITL delivery, namely: extended odd Weibull inverse Rayleigh (EOWIR) which is introduced by Almetwally [ 39 ], generalized inverse Weibull (GIW) distribution which is introduced by De Gusmao et al [ 40 ], exponential Lomax (ELo) distribution which is introduced by El-Bassiouny et al [ 41 ], modified Kies exponential (MKEx) which is introduced by Al-Babtain et al [ 21 ], and power Lomax (PL) distribution by Rady et al [ 42 ].…”

“…Bourguignon et al [ 20 ] introduced the unusual Weibull-G family. Al-Babtain et al [ 21 ] submitted a new distribution family based on the modified Kies (MK) distribution and the T-X family. A special case of the odd Weibull-G (OW) family with one parameter is the MK family.…”

A new modified Kies Fréchet distribution: Applications of mortality rate of Covid-19

“…For product moments of modified Kies (MKI) model through type II progressive censored sample, and also an approximation of model parameters [7] . Focused on the modified Kies (MKI) model family, in [8] , authors proposed a novel family of models. If is the reference CDF for a parameter vector then the MKI family CDF is defined as …”

“…Many researchers like Sindhu et al [23] , [24] modeled the COVID-19 data using new models. This study implemented two actual data implementations and concluded from modeling results that recent model is an ideal competitor with some known and popular models like the modified Kies inverted Topp-Leone (MKITL) [25] , modified Kies exponential (MKIEx) [26] , and Fréchet (F) distribution. In future research, we attempt to address a novel implementation for MKIF distribution based on a trimmed sample (see for more information Sindhu et al [27] , [28] ).…”

The Inverse-Power Logistic-Exponential Distribution: Properties, Estimation Methods, and Application to Insurance Data

“…Hence, many researcher have been interested in proposing modified forms of the exponential distribution to increase its flexibility. Some recent extensions of the exponential distribution include the exponentiated exponential [1], beta exponential [2], beta generalized exponential [3], transmuted generalized exponential [4], Harris extended exponential [5], Kumaraswamy transmuted exponential [6], Marshall-Olkin Nadarajah-Haghighi [7], modified exponential [8], alpha power exponential [9,10], odd exponentiated half-logistic exponential [11], Marshall-Olkin logistic exponential [12], generalized odd log-logistic exponential [13], Marshall-Olkin alpha power exponential [14], extended odd Weibull exponential [15], odd inverse Pareto exponential [16], modified Kies exponential [17], Topp-Leone moment exponential [18], heavy-tailed exponential [19], and odd log-logistic Lindley exponential distributions [20].…”