The normal-tangent-G class of probabilistic distributions: properties and real data modelling | [Pakistan Journal of Statistics and Operation Research • 2020]

Author(s):

1. Fa´bio V. J. Silveira: Department of Statistics and Informatics, Rural Federal University of Pernambuco, Brazil

2. Frank Gomes-Silva: Department of Statistics and Informatics, Rural Federal University of Pernambuco, Brazil

3. C´ıcero C. R. Brito: Federal Institute of Education, Science and Technology of Pernambuco, Brazil

4. Moacyr Cunha-Filho: Department of Statistics and Informatics, Rural Federal University of Pernambuco, Brazil

5. Jader S. Jale: Department of Statistics and Informatics, Rural Federal University of Pernambuco, Brazil,

6. Felipe Gusma˜o: Department of Statistics and Informatics, Rural Federal University of Pernambuco, Brazil

7. S´ılvio Xavier-Ju´ nior: Department of Statistics, Para´ıba State University, Brazil

Abstract:

This paper introduces a novel class of probability distributions called normal-tangent-G, whose submodels are parsimonious and bring no additional parameters besides the baseline's. We demonstrate that these submodels are identifiable as long as the baseline is. We present some properties of the class, including the series representation of its probability density function (pdf) and two special cases. Monte Carlo simulations are carried out to study the behavior of the maximum likelihood estimates (MLEs) of the parameters for a particular submodel. We also perform an application of it to a real dataset to exemplify the modelling benefits of the class.

Page(s): 827-838

DOI: 10.18187/pjsor.v16i4.3443

Published: Journal: Pakistan Journal of Statistics and Operation Research, Volume: 16, Issue: 4, Year: 2020

Keywords:

maximum likelihood , NormaltangentG class , Inference , Class of probabilistic distributions , Identifiable , Special submodels

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