Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

In this paper, a new probability distribution, which is synthesized based on the quasi xgamma[26] and geometric distributions, is proposed and studied. The proposed distribution so synthesized is basically a family of positively skewed probability distributions and possesses increasing and decreasing hazard rate properties depending on the values of the unknown parameters. Different important distributional and survival and/or reliability properties are also studied. A unique characterization of the distribution is presented based on reversed hazard rate. Seven different frequentist methods of estimating unknown parameters are proposed and the methods are justified with Monte-Carlo simulation study. Flexible data generation algorithm eases the utility of the proposed model in survival and/or reliability application which is accomplished by real data analyses and by comparing with other competitive life distributions.

In the most recent era, the extensions of the probability models via trigonometry methods have received great attention. This paper also offers a novel trigonometric version of the Weibull model called a type-I cosine exponentiated Weibull (for short “TICE-Weibull”) distribution. The identifiability properties for all three parameters of the TICE-Weibull model are derived. The estimators of the TICE-Weibull model are derived by implementing the maximum likelihood approach. To demonstrate the effectiveness of the TICE-Weibull model, two applications from real-world phenomena are analyzed. In addition, the proposed statistical model is established for an attribute control chart based on a time-truncated life test. The advantage of the developed charts is examined based on the average run length (ARL). The necessary tables of shift sizes and various sample sizes are offered for numerous values of the distribution parameters, as well as specified ARL and shift constants. Some numerical examples are discussed for various scheme parameters to study the performance of the new TICE-Weibull attribute control charts. According to our search and a brief study of the statistical literature, there is no published work on the development of a control chart using new probability models that are introduced using the cosine function. This is the key motivation of this work, which fills this amazing and interesting research gap.

In this paper, a new two-parameter generalized Ramos–Louzada distribution is proposed. The proposed model provides more flexibility in modeling data with increasing, decreasing, J-shaped, and reversed-J shaped hazard rate functions. Several statistical properties of the model were derived. The unknown parameters of the new distribution were explored using eight frequentist estimation approaches. These approaches are important for developing guidelines to choose the best method of estimation for the model parameters, which would be of great interest to practitioners and applied statisticians. Detailed numerical simulations are presented to examine the bias and the mean square error of the proposed estimators. The best estimation method and ordering performance of the estimators were determined using the partial and overall ranks of all estimation methods for various parameter combinations. The performance of the proposed distribution is illustrated using two real datasets from the fields of medicine and geology, and both datasets show that the new model is more appropriate as compared to the Marshall–Olkin exponential, exponentiated exponential, beta exponential, gamma, Poisson–Lomax, Lindley geometric, generalized Lindley, and Lindley distributions, among others.

We introduce a new class of continuous distributions called the generalized odd Lindley-G family. Four special models of the new family are provided. Some explicit expressions for the quantile and generating functions, ordinary and incomplete moments, order statistics and Rényi and Shannon entropies are derived. The maximum likelihood method is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.