A new three-parameter generalized distribution, namely, half-logistic generalized Weibull (HLGW) distribution, is proposed. The proposed distribution exhibits increasing, decreasing, bathtub-shaped, unimodal, and decreasing-increasing-decreasing hazard rates. The distribution is a compound distribution of type I half-logistic-G and Dimitrakopoulou distribution. The new model includes half-logistic Weibull distribution, half-logistic exponential distribution, and half-logistic Nadarajah-Haghighi distribution as submodels. Some distributional properties of the new model are investigated which include the density function shapes and the failure rate function, raw moments, moment generating function, order statistics, L-moments, and quantile function. The parameters involved in the model are estimated using the method of maximum likelihood estimation. The asymptotic distribution of the estimators is also investigated via Fisher's information matrix. The likelihood ratio (LR) test is used to compare the HLGW distribution with its submodels. Some applications of the proposed distribution using real data sets are included to examine the usefulness of the distribution.
We introduce a new two-parameter lifetime distribution called the half-logistic Lomax (HLL) distribution. The proposed distribution is obtained by compounding half-logistic and Lomax distributions. We derive some mathematical properties of the proposed distribution such as the survival and hazard rate function, quantile function, mode, median, moments and moment generating functions, mean deviations from mean and median, mean residual life function, order statistics, and entropies. The estimation of parameters is performed by maximum likelihood and the formulas for the elements of the Fisher information matrix are provided. A simulation study is run to assess the performance of maximum-likelihood estimators (MLEs). The flexibility and potentiality of the proposed model are illustrated by means of real and simulated data sets.
In this study, we propose a two stage randomized response model. Improved unbiased estimators of the mean number of persons possessing a rare sensitive attribute under two different situations are proposed. The proposed estimators are evaluated using a relative efficiency comparison. It is shown that our estimators are efficient as compared to existing estimators when the parameter of rare unrelated attribute is known and in unknown case, depending on the probability of selecting a question.
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