The present paper proposes a new distribution called the inverse power logistic exponential distribution that extends the inverse Weibull, inverse logistic exponential, inverse Rayleigh, and inverse exponential distributions. The proposed model accommodates symmetrical, right-skewed, left-skewed, reversed-J-shaped, and J-shaped densities and increasing, unimodal, decreasing, reversed-J-shaped, and J-shaped hazard rates. We derive some mathematical properties of the proposed model. The model parameters were estimated using five estimation methods including the maximum likelihood, Anderson–Darling, least-squares, Cramér–von Mises, and weighted least-squares estimation methods. The performance of these estimation methods was assessed by a detailed simulation study. Furthermore, the flexibility of the introduced model was studied using an insurance real dataset, showing that the proposed model can be used to fit the insurance data as compared with twelve competing models.

In this paper, a new modified version of geometric distribution is proposed. The newly introduced model is called transmuted record type geometric (TRTG) distribution. TRTG distribution is a good alternative to the negative binomial, Poisson and geometric distributions in modeling real data encountered in several applied fields. The main statistical properties of the new distribution were obtained. We determined the measures of value at risk and tail value at risk for the TRTG distribution. These measures are important quantities in actuarial sciences for portfolio optimization under uncertainty. The TRTG parameters were estimated via maximum likelihood, moments, proportions, and Bayesian estimation methods, and the simulation results were determined to explore their performance. Furthermore, a new count regression model based on the TRTG distribution was proposed. Four real data applications were adopted to illustrate the applicability of the TRTG distribution and its count regression model. These applications showed empirically that the TRTG distribution outperforms some important discrete models such as the negative binomial, transmuted geometric, discrete Burr, discrete Chen, geometric, and Poisson distributions.

The present article introduces a new distribution called the odd log–logistic Lindley-Weibull (OLLLW) distribution that provides greater flexibility in modeling data in applied areas such as medicine and engineering. The OLLLW model provides left-skewed, symmetric, right-skewed, and reversed-J shaped densities. Its hazard function can be bathtub, unimodal, increasing or decreasing. The OLLLW density was expressed as a linear mixture of Weibull densities. Some distributional properties of the introduced model are derived. Its parameters are estimated using five classical estimators called, the maximum likelihood, Anderson–Darling, least-squares, Cramér-von Mises, and weighted least squares estimators. The performance of the proposed estimators is explored by detailed simulation results. The flexibility of the OLLLW distribution is studied by two real data sets from medicine and engineering sciences, showing that its capability to fit the data effectively than the Weibull, Fréchet Weibull, transmuted Weibull, gamma Weibull, transmuted exponentiated Weibull, and modified Weibull distributions.

This article considers unbiased estimation of mean, variance and sensitivity level of a sensitive variable via scrambled response modeling. In particular, we focus on estimation of the mean. The idea of using additive and subtractive scrambling has been suggested under a recent scrambled response model. Whether it is estimation of mean, variance or sensitivity level, the proposed scheme of estimation is shown relatively more efficient than that recent model. As far as the estimation of mean is concerned, the proposed estimators perform relatively better than the estimators based on recent additive scrambling models. Relative efficiency comparisons are also made in order to highlight the performance of proposed estimators under suggested scrambling technique.

The present article introduces a new distribution called the modified Kies-Fréchet (MKF) distribution that extends the Fréchet distribution and provides two new sub-models called modified Kies inverse-exponential and modified Kies inverse-Rayleigh distributions. The MKF model can provide left-skewed, symmetrical, right-skewed, J-shaped, and reversed-J shaped densities. The MKF density was expressed as a linear combination of Fréchet densities. We derive some basic mathematical properties of the MKF model. The MKF parameters are estimated using some classical estimation methods called, the maximum likelihood, Anderson-Darling, least-squares, Cramér-von Mises, and weighted least squares. The performances of these estimators were explored by a detailed simulation study. Finally, the flexibility of the MKF model is checked using a real data set, showing that it can provide close fit as compared with other competing models.

One of the important features of generalized distribution is its ability and flexibility to model real-life data in several applied fields such as medicine, engineering, and survival analysis, among others. In this paper, a flexible four-parameter Lomax extension called the alpha-power power-Lomax (APPLx) distribution is introduced. The APPLx distribution is analytically tractable, and it can be used quite effectively for real-life data analysis. Key mathematical properties of the APPLx distribution including mode, moments, stress-strength reliability, quantile and generating functions, and order statistics are presented. The APPEx parameters are estimated by using eight classical estimation methods. Extensive simulation studies are provided to explore the performance of the proposed estimation methods and to provide a guideline for practitioners and engineers to choose the best estimation method. Three real-life datasets from applied fields are fitted to assess empirically the flexibility of the APPLx distribution. The APPLx distribution shows greater flexibility as compared to the McDonal–Lomax, Fréchet Topp–Leone Lomax, transmuted Weibull–Lomax, Kumaraswamy–Lomax, beta exponentiated-Lomax, Weibull–Lomax, Burr-X Lomax, Lomax–Weibull, odd exponentiated half-logistic Lomax, and alpha-power Lomax distributions.