A New Class of the Failure Quantile Models with Increasing, Decreasing and Bathtub-Shaped Failure Rates

The article considers a new áexible distribution with di§erent shape of quan- tile hazard rate. A new class developed is the sum of quantile functions of the generalized extreme value and weibull distributions. A new model has the probability density function whose sensitive skewness is a general case of prob- ability density quantile function of the exponential distribution, probability density quantile function of the rayleigh distribution, exponential distribution and rayleigh distribution. Di§erent properties and reliability characterization of this new model have been discussed and inference of parameters using per- centile methods and L-moments methods are studied. To clarify the procedure of methods of estimation, two real data sets were performed.