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Power analysis of several normality tests: A Monte Carlo simulation study
Abstract
In statistical inference, oftentimes the data are assumed to be normally distributed. Consequently, testing the validity of the normality assumption is an integral part of such statistical analyses. Here, we investigate twelve currently available tests for normality using Monte-Carlo simulation. Alternative distributions are used to calculate the empirical power of the tests studied here. The distributions considered arise from three different categories: symmetric short-tailed, symmetric long-tailed and asymmetric. In addition, power is calculated for several contaminated alternatives. As a direct consequence of this study, we recommend a two-tier approach: (i) observe the shape of the empirical data distribution using graphical methods, then (ii) select an appropriate test based on the likely distributional shape and the corresponding sample size. In general, with respect to power considerations, it is observed that for asymmetric distributions, the Shapiro-Wilk and Ryan-Joiner tests perform fairly well for all sample sizes studied here. Additionally, the Jarque-Bera, Modified Jarque-Bera, and Ryan-Joiner tests perform fairly well for contaminated normal distributions. The popular methods available in current software packages, such as the Shapiro-Wilk test, the Ryan-Joiner Normality test, and the Anderson-Darling goodness of test, work at least moderately well for most of the cases we considered.
Keywords
- Normality test;
- Skewed distributions;
- Monte Carlo Simulation;
- Assumptions of Normality;
- Power comparison;
Generalized confidence limits for the performance index of the exponentially distributed lifetime
Abstract
Under a two-parameter exponential distribution, this study constructs the generalized lower confidence limit of the lifetime performance index CL based on type-II right-censored data. The confidence limit has to be numerically obtained; however, the required computations are simple and straightforward. Confidence limits of CL computed under the generalized paradigm are compared with those of CL computed under the classical paradigm, citing an illustrative example with real data and two examples with simulated data, to demonstrate the merits and advantages of the proposed generalized variable method over the classical method.
Keywords
- Classical lower confidence bound;
- Generalized lower confidence bound;
- Lifetime performance index;
- Shifted-exponential distribution.
Tests Based on Kurtosis for Multivariate Normality
Abstract
In this paper, we first transform a multivariate normal random vector into a random vector with elements that are approximately independent standard normal random variables. Then we propose the multivariate version generalized from the univariate normality test based on kurtosis from the literature. Power is investigated through the Monte Carlo Simulation with different significance level, dimension, and sample size. To assess the validity and accuracy of the new tests, we carry a comparative study with several other existing tests by selecting certain types of symmetric and asymmetric alternative distributions.
Keywords
- transformation;
- multivariate normal;
- Pearson kurtosis;
- Monte Carlo simulation.
Implementing a Lifetime Performance Index of Products with a Two-ParameterRayleigh Distribution Under a Progressively Type II Censored Sample
Abstract
In manufacturing, quality control is a process that ensures customers receive products free from defects and meet their needs. Process capability analysis has been widely applied in the field of quality control to find out how well a given process meets a set of specification limits. The lifetime performance index C_L a type of process capability index is used to measure the larger-the-better type quality characteristics. Under the assumption of Two-Parameter Rayleigh Distribution, this study constructs a maximum likelihood estimator of C_L based on the progressively type II right censored sample. The maximum likelihood estimator of C_L is then utilized to develop the new hypothesis testing procedure. The testing procedure can be employed the testing procedure to determine whether the lifetime of a product adheres to the required level.
Keywords
- Lifetime Data;
- Lifetime Performance Index;
- lower specification limit;
- progressive type II censored sample.
Assessing the lifetime performance index of products with two-parameter Rayleigh Distribution under progressively type II right censored samples
Abstract
In practice, process capability indices (PCIs) are widely used in the field of quality control. The lifetime performance index (CL) is used to measure process potential and performance, where L is the lower specification limit. In this paper, we apply data transformation technology to construct a maximum likelihood estimator (MLE) of CL under the two-parameter Rayleigh distribution based on the progressively type II right censored sample. The MLE of CL is then utilized to develop a hypothesis testing procedure. Finally, we give the Monte Carlo power simulation to assess the behavior of the lifetime perform index.
Keywords
- Process capability index;
- The lifetime performance index;
- Progressive type II right censored sample;
- Maximum likelihood estimator;
- Two-parameter Rayleigh Distribution.
Lifetime performance index of Truncated Extreme Value Distribution using progressive type II right censored samples
Abstract
Assessing lifetime performance index is a crucial subject of discourse in manufacturing industries. In this paper, we construct various point and interval estimators of the lifetime performance index based on progressive type II right censored data for Truncated Extreme Value Distribution based on classical setup. In addition, we propose problems concerning the lifetime performance index (CL ) and perform Monte Carlo simulations to compare the performances of the Maximum likelihood of CL under different censoring schemes.
Keywords
- Truncated Extreme Value distribution;
- Lifetime performance index;
- Maximum likelihood;
- Monte Carlo simulation;
- progressive type II Right Censored Data.
Classification of all-rounders in limited over cricket - a machine learning approach
Abstract
In cricket, all-rounders play an important role. A good all-rounder should be able to contribute to the team by both bat and ball as needed. However, these players still have their dominant role by which we categorize them as batting all-rounders or bowling all-rounders. Current practice is to do so by mostly subjective methods. In this study, the authors have explored different machine learning techniques to classify all-rounders into bowling all-rounders or batting all-rounders based on their observed performance statistics. In particular, logistic regression, linear discriminant function, quadratic discriminant function, na ¨ıveBayes,support vector machine, and random forest classification methods were explored. Evaluation of the performance of the classification methods was done using the metrics accuracy and area under the ROC curve. While all the six methods performed well, logistic regression, linear discriminant function, quadratic discriminant function, and support vector machine showed out standing performance suggesting that these methods can be used to develop an automated classification rule to classify all-rounders in cricket. Given the rising popularity of cricket, and the increasing revenue generated by the sport, the use of such a prediction tool could be of tremendous benefit to decision-makers in cricket.
Keywords
- Classification;
- machine learning;
- statistical learning;
- cricket;
- all-rounders;
- ranking.