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

Additive and subtractive scrambling in optional randomized response modeling.

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

General Randomized Response Techniques Using Polya's Urn Process as a Randomization Device

<div><p>In this paper, interesting improvements in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115612#pone.0115612-Kuk1" target="_blank">[1]</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115612#pone.0115612-Singh1" target="_blank">[2]</a> randomized response techniques have been proposed. The proposed randomized response technique applies Polya's urn process (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115612#pone.0115612-Mahmoud1" target="_blank">[3]</a>) to obtain data from respondents. One of the suggested technique requires reporting the number of draws to observe a fixed number of cards of certain type. On the contrary, the number of cards of a certain type is to be reported in case of second proposed randomized response model. Based on the information collected through the suggested techniques, two different unbiased estimators of proportion of a sensitive attribute have been suggested. A detailed comparative simulation study has also been done. The results are also supported by means of a small scale survey.</p></div

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A Novel Extended Power-Lomax Distribution for Modeling Real-Life Data: Properties and Inference

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