Tolerancing conducted by design engineers to meet customers’ needs is a prerequisite for producing high-quality products. Engineers use handbooks to conduct tolerancing. While use of statistical methods for tolerancing is not something new, engineers often use known distributions, including the normal distribution. Yet, if the statistical distribution of the given variable is unknown, a new sta...

The method of moments is a popular technique for estimating the parameters of a generalized lambda distribution (GLD), but published results suggest that the percentile method gives superior results. However, the percentile method cannot be implemented in an automatic fashion, and automatic methods, like the starship method, can lead to prohibitive execution time with large sample sizes. A new ...

In this paper, we investigate the goodness-of-fit of flexible four-parameter generalized Lambda Distribution (GLD) for high-frequency 5-min returns sampled from DJI30 Index. Applying Moment Matching (MM) and Maximum Likelihood Estimation (MLE) techniques, highlight significance higher-order parameters GLD distribution to depict asymmetric fat-tailed behaviour observed in data. We also show expl...

This paper considers the application of method of percentile matching available in statistical theory of estimation for estimating the parameters involved in uncertainty distributions. An empirical study has been carried out to compare the performance of the proposed method with the method of moments and the method of least squares considered by Wang and Peng (J. Uncertainty Analys. Appl. 2, (2...

The 4-parameter generalized lambda distribution (GLD) is a flexible distribution capable of mimicking the shapes of many distributions and data samples including those with heavy tails. The method of L-moments and the recently developed method of trimmed L-moments (TL-moments) are attractive techniques for parameter estimation for heavy-tailed distributions for which the Land TL-moments have be...

The generalized lambda distribution (GLD) is a flexible distribution for statistical modelling, but existing estimation methodologies for the GLD are computationally difficult, rendering the GLD impractical for many practitioners. We derive a parameterization of the GLD with closed-form expressions for the method of L-moment estimators. A numerical example involving the age of coronary heart di...

Tolerancing is one of the most important tools for planning, controlling, and improving quality in the industry. Tolerancing conducted by design engineers to meet customers’ needs is a prerequisite for producing high-quality products. Engineers use handbooks to conduct tolerancing. While use of statistical methods for tolerancing is not a new concept, engineers often use known distributions, in...

The generalized lambda distribution (GLD) is a flexible four parameter distribution with many practical applications. L-moments of the GLD can be expressed in closed form and are good alternatives for the central moments. The L-moments of the GLD up to an arbitrary order are presented, and a study of L-skewness and L-kurtosis that can be achieved by the GLD is provided. The boundaries of L-skew...