T-normal family of distributions: a new approach to generalize the normal distribution

By Ayman Alzaatreh, Carl Lee, Felix Famoye. 2014

110 citations recorded by the source corpus.

The idea of generating skewed distributions from normal has been of great interest among researchers for decades. This paper proposes four families of generalized normal distributions using the T-X framework. These four families of distributions are named as T-normal families arising from the quantile functions of (i) standard exponential, (ii) standard log-logistic, (iii) standard logistic and (iv) standard extreme value distributions. Some general properties including moments, mean deviations and Shannon entropy of the T-normal family are studied. Four new generalized normal distributions are developed using the T-normal method. Some properties of these four generalized normal distributions are studied in detail. The shapes of the proposed T-normal distributions can be symmetric, skewed to the right, skewed to the left, or bimodal. Two data sets, one skewed unimodal and the other bimodal, are fitted by using the generalized T-normal distributions.AMS 2010 Subject Classification60E05; 62E15; 62P10

Subfields: Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b04b8e1200724df9606ca34ed3c622f5db8e8b98

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Global and Planetary Change

1. Mohamed E. Mead
2. Mazen Nassar
3. Osama E. Abo-Kasem
4. Ayman Alzaatreh

In Statistics and Probability

1. Mohamed E. Mead
2. Mazen Nassar
3. Osama E. Abo-Kasem
4. Ayman Alzaatreh

Citations in the corpus

• The Kumaraswamy Marshal-Olkin family of distributions (2015, unknown): “[17], LomaxG by Cordeiro et al.”
• Alpha power Weibull distribution: Properties and applications (2017, methodology): “For recent methods of generalized continuous and discrete distributions, we refer the reader to Lee et al. (2013) and Alzaatreh et al. (2014).”
• The generalized Cauchy family of distributions with applications (2016, unknown): “The beta-generated family was extended by Alzaatreh et al. (2013) to the T -”
• A New Weibull-G Family of Distributions (2015, unknown): “[5], Lomax-G by Cordeiro et al.”