The Theoretical Overview of Generalized Gumbel Type-Ⅱ Distribution
S. Qurat Ul Ain *
Department of Mathematics, Bhagwant University, Rajasthan, India.
Ahmad Aijaz
Department of Mathematics, Bhagwant University, Rajasthan, India.
Rajnee Tripathi
Department of Mathematics, Bhagwant University, Rajasthan, India.
*Author to whom correspondence should be addressed.
Abstract
A new version of weighted model is introduced by assigning weights to Gumbel Distribution Type Ⅱ (GDT-Ⅱ) to make it more useful and flexible in life time data .This paper provides an understanding of some basic statistical properties of (WGDT-Ⅱ).It includes moments and maximum likelihood estimator. In addition to the above it imparts the insight to distribution function, survival rate, hazard rate and reverse hazard rate. The behavior of PDF, CDF, and Survival rate, Hazard rates and Reverse Hazard rates has been presented through various graphs by setting different values of parameters.
Keywords: Gumbel distribution Type-Ⅱ, weighted distribution, maximum likelihood estimator, survival function, hazard rate, reverse hazard rate.