Open Access Research article

A Chen Type Generated Family of Distributions

Clement Boateng Ampadu*

1Department of Biostatistics, 31 Carrolton Road, Boston MA 02132-6303, USA

Corresponding Author

Received Date: March 04, 2020;  Published Date: March 19, 2020


Inspired by [1] and [2] we introduce a new Chen type generated family of distributions and show a sub-model of this broad class of statistical distributions is a good fit to real-life data. Our hope is that readers will consider investigating some properties and applications of this new class of distributions.


The New Family Illustrated

We begin with the following

Definition 2.1.1: Let T be a random variable with PDF g (t ) and CDF G(t ), and let X be a random variable with CDF F (x) ,the new Chen generated family of distributions (“ CT − X ” for short) is defined by the following integral for its CDF


the Proposition immediately above we have the following Theorem 2.1.3: The CDF of Chen Exponential-Normal is given by


Obviously, the PDF can be obtained upon differentiating the CDF above. We write W ∼ CEN(λ,β ,c, d, f ) , if W is a Chen Exponential-Normal random variable. The Chen Exponential Normal distribution is a good fit to real life data as shown below [Figure 1].



Conflict of Interest

No conflict of interest.


  1. Ampadu CB (2019) The AT-Transmuted-X Family of Distributions. Adv Ind Biotechnol 2: 06.
  2. Lea Anzagra, Solomon Sarpong, Suleman Nasiru (2020) Chen-G class of distributions, Cogent Mathematics & Statistics.
  3. Ayman Alzaatreh, Carl Lee, Felix Famoye (2014) T-normal family of distributions: a new approach to generalize the normal distribution. Journal of Statistical Distributions and Applications 1: 16.
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