This article presents a novel and powerful goodness-of-fit test specifically designed for the Cauchy distribution.The motivation behind our research stems from the need for a more accurate and robust method to assess the fit of the Cauchy distribution to data.This distribution is known for its heavy tails and lack of finite moments.To compute the proposed test statistic, we utilize the maximum likelihood estimators of the unknown parameters, ensuring the test efficiency and reliability.In addition, Monte Carlo simulations are employed to obtain critical points of the test statistic for different sample sizes, enabling precise determination of the threshold for rejecting the null hypothesis.To assess the performance of the proposed test, we conduct power comparisons against several well-known competing tests, considering various alternative distributions.Through extensive simulations, we demonstrate the superiority of our test in the majority of the cases examined, highlighting its effectiveness in distinguishing departures from the Cauchy distribution.The contributions of our study are twofold.Firstly, we introduce a novel goodness-of-fit test tailored specifically for the Cauchy distribution, taking into account its unique characteristics.By incorporating the maximum likelihood estimate and employing Monte Carlo simulations, our test offers improved accuracy and robustness compared to existing methods.Furthermore, we provide practical validation of the proposed test through the analysis of a financial dataset.The application of the test to real-world data underscores its relevance and applicability in practical scenarios.

The asymptotic distributions of likelihood ratio tests for normality are unknown; only a few critical values have been tabulated using Monte Carlo simulations.This study aims to develop the critical value functions for these likelihood ratio tests using response surface regressions.In these regressions, the simulated critical values depend on sample size; however, practitioners can easily compute the finite-sample critical values for a number of sample sizes using a hand calculator.An extensive Monte Carlo simulation shows that the proposed critical value functions perform very well for both small and large samples.

Statistical process control is extensively applied for monitoring the production process. One of the important tools of statistical process control for detecting the unusual changes in the manufacturing process is the control chart. In the use of a control chart, samples or subgroups are selected in a manner that if unusual changes are present, the chance for differences between subgroups will be maximized, while the chance for differences within a subgroup will be minimized. However, there are different practical engineering processes where this assumption would not be applicable. In this paper, we considered a Wind Energy process where differences within a subgroup are significant and proposed a new control chart namely Ladder Ascending Control Chart under this situation. The Ladder Ascending Control Chart is based on order statistics by using order statistic distribution as the underlying distribution. Shewhart type control limits formulae for the order statistic mean have been built. It is applied to wind energy for monitoring the wind speed using the Weibull distribution as the underlying distribution of wind speed. The average run length is provided as a performance measure for the Ladder Ascending Control Chart. A real-life example is provided for its application and interpretation.

In the realm of astronomy, the two-parameter log-normal distribution has ominous implications. In this article, we propose a new version of the two-parameter log-normal distribution with an application to astronomical data. More precisely, a new modulating parameter is added to the two-parameter log-normal distribution through the use of the Topp-Leone generator of distributions. The moments, quantile function, several reliability measures, and other significant aspects of the proposed distribution are investigated. The maximum likelihood approach and a Bayesian technique are both utilized to estimate the unknown parameters. In addition, we present a parametric regression model and a Bayesian regression method. A simulation study is carried out to assess the long-term performance of the estimators of the distribution parameters. Two real datasets are employed to show the applicability of this new distribution. The e ciency of the newly added parameter is tested by utilizing the likelihood ratio test. The parametric bootstrap approach is also utilized to determine the adequacy of the suggested model for the datasets.

In this paper, the McDonald-Chen distribution is proposed and studied to model different type of data.Its probability density function allows bimodality, thus showing that the model is very flexible.Its failure or hazard rate function may have increasing, decreasing, bathtub, inverted bathtub and increasing-decreasing-increasing shapes depending on the parameter values.The new distribution includes at least five major special cases.Some of its mathematical properties are addressed.The maximum likelihood method is adopted to estimate the model parameters.Monte Carlo simulations evaluate the accuracy of the maximum likelihood estimators.The new distribution is better than three other popular distributions to model two real data sets.