In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.

Recently, the Darna distribution has been introduced as a new lifetime distribution. The two-parameter Darna distribution represents is a mixture of two well-known gamma and exponential distributions. A manufacturer or an engineer of products conducts life testing to examine whether the quality level of products meets the customer’s requirements, such as reliability or the minimum lifetime. In this article, an attribute modified chain sampling inspection plan based on the time truncated life test is proposed for items whose lifetime follows the Darna distribution. The plan parameters, including the sample size, the acceptance number, and the past lot result of the proposed sampling plan, are determined with the help of the two-point approach considering the acceptable quality level (AQL) and the limiting quality level (LQL). The plan parameters and the corresponding operating characteristic functions of a new plan are provided in tabular form for various Darna distribution parameters. Also, a few illustrated examples are presented for various distribution parameters. The usefulness of the proposed attribute modified chain sampling plan is investigated using two real failure time datasets. The results indicate that the proposed sampling plan can reduce the sample size when the termination ratio increases for fixed values of the producer’s risk and acceptance number. Hence, the proposed attribute modified chain sampling inspection plan is recommended to practitioners in the field.

In this paper, we develop new acceptance sampling plans based on truncated life tests for the Akash distribution. With various values of the Akash distribution parameter, the minimum sample sizes required to assert the specified mean life are obtained, also the operating characteristic function values and producer’s risk of the proposed sampling plan are presented. The results are illustrated by different examples for different values of the sampling plans. A real data of 20 small electric carts is used to illustrate the power of the new sampling plans. The results revealed that the suggested acceptance sampling plan is useful for researchers and engineering in producing lots.

The ordinary least square (OLS) method is commonly used in regression analysis. But in the presence of outlier in the data, its results are unreliable. Hence, the robust regression methods have been suggested for a long time as alternatives to the OLS to solve the outliers problem. In the present study, new ratio type estimators of finite population mean are suggested using simple random sampling without replacement (SRSWOR) utilizing the supplementary information in Bowley’s coefficient of skewness with quartiles. For these proposed estimators, we have used the OLS, Huber-M, Mallows GM-estimate, Schweppe GM-estimate, and SIS GM-estimate methods for estimating the population parameters. Theoretically, the mean square error (MSE) equations of various estimators are obtained and compared with the OLS competitor. Simulations for skewed distributions as the Gamma distribution support the results, and an application of real data set containing outliers is considered for illustration.

In this paper, a new modified Kumaraswamy distribution is proposed, and some of its basic properties are presented, such as the mathematical expressions for the moments, probability weighted moments, order statistics, quantile function, reliability, and entropy measures. The parameter estimation is done via the maximum likelihood estimation method. In order to show the usefulness of the proposed model, some well‐established actuarial measures such as value‐at‐risk, expected‐shortfall, tail‐value‐at‐risk, tail‐variance, and tail‐variance‐premium are obtained. A simulation study is carried out to assess the performance of maximum likelihood estimates. The empirical analysis is carried out to show that our proposed model is better in performance as compared to other competitive models related to the extended Kumaraswamy model. Thus, insurance claim data and engineering related real‐life data sets are considered to prove this claim.

In this article, we study some properties of a new distribution, namely Exponentiated Ailamujia distribution (EAD). The Exponentiated Ailamujia has two parameters (scale and shape). The different structural properties of the EAD have been obtained as the moments, reliability analysis, and the harmonic mean. The parameters of the proposed model are estimated through the maximum likelihood method. Real life medical data sets are considered to show that the exponentiated Ailamujia distribution has a better fit as compared to the Ailamujia and Lindley distributions.