Bounded Inverse-Slashed Pareto Model: Structural Properties and Real-Life Applications
Keywords:
Probability model, Moments; Distribution, Maximum Likelihood EstimationAbstract
A novel probability model with bounded support is introduced. The formulation of this new probability model is based on inverting the Slashed Pareto distribution. This new distribution has the merit of being very simple and not involving any complex mathematical function in its construction. Some interesting properties like moments, skewness and kurtosis, unimodality, L-Moments, L-skewness and L-kurtosis would be explored in detail. Various Survival properties including survival function, hazard rate function and mean residual life(MRL) like have been given. For estimating the parameters contained in the new model, methods like Method of Moments (MOM) and Maximum Likelihood Estimation (MLE) have been used.
References
H. Akaike, A new look at the statistical model identification. IEEE Transactions on Automatic Control, 1974;19(6): 716–723.
S. Kotz, J.R. van Dorp, Beyond Beta; Other Continuous Families of Distributions With Bounded Support and Applications, 2004, World Scientific, New Jersey.
C. Armero, M.J. Bayarri, Prior assessments for prediction in queues. The Statistician, 1994;43: 139–153.
M.B. Gordy, Computationally convenient distributional assumptions for common-value auctions. Computational Eco-nomics, 1998;12:61–78.
E. G´omez-D´eniz, M. A. Sordo, E. Calder´n-Ojeda, The LogLindley distribution as an alternative to the beta regression model with applications in insurance. Insurance: Mathematics and Economics, 2014; 54:49–57.
A. Grassia, On a family of distributions with argument between 0 and 1 obtained by transformation of the gamma and derived compound distributions. The Australian Journal of Statistics, 1997;19 (2):108–114.
M.C. Jones, Kumaraswamys distribution: a beta-type distribution with some tractability advantages. Statistical Method-ology 2009: 70–81.
J.B. McDonald, Some generalized functions for the size distribution of income. Econometrica, 1984;52:647–664.
G. P. Patil, M. V. Ratnaparkhi, Weighted Distributions and Size-Biased Sampling with Applications to Wildlife Populations and Human Families. Biometrics, 1978;34:179–189.
G. Schwarz, Estimating the dimension of a model. Annals of Statistics, 1978;6(2):461–464.
