On the Gumbel-Burr XII Distribution: Regression and Application

In this article, additional properties of the Gumbel-Burr XII distribution, denoted by (GBXII(L)), defined in (Osatohanmwen et al., 2017), are studied. We consider some useful characterizations for the GBXII(L) distribution and some of its properties. A simulation study is conducted to assess the performance of the MLEs and the usefulness of the GBXII(L) distribution is illustrated by means of three real data sets. The simulation study suggests that the maximum likelihood method can be used to estimate the distribution parameters, and the three examples show that the GBXII(L) is very flexible in fitting different shapes of data. A log-GBXII(L) regression model is proposed and a survival data is used in an application of the proposed regression model. The log-GBXII(L) regression model is adequate and can be used in comparison to other models

On the Burr XII-Power Cauchy Distribution: Properties and Applications

We propose a new four-parameter lifetime model with flexible hazard rate called the Burr XII Power Cauchy (BXII-PC) distribution. We derive the BXII-PC distribution via (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The new proposed distribution is flexible as it has famous sub-models such as Burr XII-half Cauchy, Lomax-power Cauchy, Lomax-half Cauchy, Log-logistic-power Cauchy, log-logistic-half Cauchy. The failure rate function for the BXII-PC distribution is flexible as it can accommodate various shapes such as the modified bathtub, inverted bathtub, increasing, decreasing; increasing-decreasing and decreasing-increasing-decreasing. Its density function can take shapes such as exponential, J, reverse-J, left-skewed, right-skewed and symmetrical. To illustrate the importance of the BXII-PC distribution, we establish various mathematical properties such as random number generator, moments, inequality measures, reliability measures and characterization. Six estimation methods are used to estimate the unknown parameters of the proposed distribution. We perform a simulation study on the basis of the graphical results to demonstrate the performance of the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling estimators of the parameters of the BXII-PC distribution. We consider an application to a real data set to prove empirically the potentiality of the proposed model

Decentralized fractional order control scheme for LFC of deregulated nonlinear power systems in presence of EVs and RER

Load frequency control scheme is one of the main control procedures in large electric grids incorporating electric vehicles. Load frequency control controllers play an important role in maintaining both the frequency in each area and the exchanged power between the different areas in permissible range. With moving conventional power systems toward the smart grid concept, the penetration level of electric vehicles and renewable energy resources has been rapidly increased. With such a growth in renewable energy sources integration into the grid, controlling the load frequency is a major operational challenge encountered in electric grids necessitating to be carefully investigated. To this end, a new fractional order control scheme is designed for the interconnected power systems considering the deregulation environment. The fractional order controller is characterized with a higher freedom degree compared to the conventional that make it possible to have a much better control performance. Also, the participation of electric vehicles in providing a secondary power reserve for a future smart grid is studied in this paper. The controllers' parameters are tuned via several evolutionary algorithms such as imperialist competitive algorithm, differential algorithm and others. Several numerical analyses are performed to evaluate the effectiveness of the control scheme that is proposed in this paper. Likewise, the effectiveness of electric vehicles and renewable generation's participation in load frequency control is examined

A Novel Accelerated Failure Time Model: Characterizations, Validation Testing, Different Estimation Methods and Applications in Engineering and Medicine

In this paper, we present a new exponential accelerated failure time model. Some of its properties and characterization results are derived. Different estimation methods are considered for assessing the finite sample behaviour of the estimators. Simulation studies for comparing the estimation methods are performed. Finally, we present a novel modified chi-square test for the novel exponential accelerated failure time model in both complete and right censored data cases. The validity of the new model is checked by using the theoretical global of the Nikulin-Rao-Robson. The maximum likelihood method is considered for this purpose. Two simulation studies are performed to assess the exponential accelerated failure time model and the efficiency of the Nikulin-Rao-Robson test statistic, respectively. Three real data sets are considered for illustrating the efficiency of the test statistic in validation