The Tukey g ‐and‐ h distribution

Tukey g-and-h Random Fields

We propose a new class of trans-Gaussian random fields named Tukey g-and-h (TGH) random fields to model non-Gaussian spatial data. The proposed TGH random fields have extremely flexible marginal distributions, possibly skewed and/or heavy-tailed, and, therefore, have a wide range of applications. The special formulation of the TGH random field enables an automatic search for the most suitable t...

Non-Gaussian Autoregressive Processes with Tukey g-and-h Transformations

When performing a time series analysis of continuous data, for example from climate or environmental problems, the assumption that the process is Gaussian is often violated. Therefore, we introduce two non-Gaussian autoregressive time series models that are able to fit skewed and heavy-tailed time series data. Our two models are based on the Tukey g-and-h transformation. We discuss parameter es...

Estimating Process Capability Indices Using Univariate g and h Distribution

Process capability of a process is defined as inherent variability of a process which is running under chance cause of variation only. Process capability index is measuring the ability of a process to meet the product specification limit. Generally process capability is measured by 6 assuming that the product characteristic follows Normal distribution. In many practical situations the product ...

Simulating Univariate and Multivariate Tukey g-and-h Distributions Based on the Method of Percentiles

The Cooley–Tukey FFT and Group Theory

In 1965 J. Cooley and J. Tukey published an article detailing an efficient algorithm to compute the Discrete Fourier Transform, necessary for processing the newly available reams of digital time series produced by recently invented analog-to-digital converters. Since then, the Cooley– Tukey Fast Fourier Transform and its variants has been a staple of digital signal processing. Among the many ca...