Abstract
Recently, Sarhan (2009) introduced a new distribution named generalized quadratic hazard rate distribution. In this study, we define a bivariate Generalized Quadratic Hazard Rate Distribution (BGQHRD). The joint cumulative distribution function and joint survival function are derived in compact forms. Several properties of BGQFRD have been discussed. The conditional probability density function, rth moments and joint and marginal moment generating functions are obtained. Parameters estimators using the maximum likelihood method are obtained. A numerical illustration is used to obtain maximum likelihood estimators (MLEs). Moreover, we study the behavior of the estimators numerically.
Highlights
Sarhan (2009) introduced a new distribution named generalized quadratic hazard rate distribution
This paper introduces a Bivariate Generalized Quadratic Hazard Rate Distribution (BGQHRD) by using the method of Marshall and Olkin (1986)
We start with the joint cumulative distribution function of the distribution
Summary
Sarhan (2009) introduced a new distribution named generalized quadratic hazard rate distribution. This paper introduces a Bivariate Generalized Quadratic Hazard Rate Distribution (BGQHRD) by using the method of Marshall and Olkin (1986). The GQHRD may have an decreasing (increasing) hazard or a bathtub shaped hazard or an upside-down bathtub shaped hazard function This property enables this distribution to be used in many applications such as in reliability, life testing, survival analysis. The random variable X has the Quadratic Hazard Rate Distribution (QHRD) with parameters a, b, c if its Cumulative Distribution Function (CDF) is: F ( x; a, b, c). Sarhan (2009) introduced the generalized quadratic hazard rate distribution with parameters a, b, c and d, (GQHRD(a,b,c,d)).
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