A new flexible hazard rate distribution: Application and estimation of its parameters

The Lomax-Lindley distribution: properties and applications to lifetime data

“…To obtain more flexible models with simple hazard rate functions, a useful technique is combining the hazard rates of two distributions. For example, additive Weibull distribution by Xie and Lai [25], new modified Weibull distribution by Almalki and Yuan [4] and power-exponential hazard rate distribution by Tarvirdizade and Nematollahi [24] are some models introduced by using this technique. The goal of this article is to propose a new three-parameter lifetime distribution called the Lomax-Lindley (L-L) distribution using the combination of the Lomax and the Lindley distributions in a serial system.…”

“…Some programs developed in R for the L-L distribution fitting and estimation of its parameters are given as follows: library(MASS) # LHD data x=c (110,13,72,4,45,56,19,27,36,90,19,7,2,118,44,8,277,4,8,10,79,103,6,18,147,96,22,3,24,3,9,99,82,121,54,79,99,18,5,21,1,3,5,1,59,22,17,35,35,29) n=50 logL=function(par){ al=par [1] be=par [2] te=par [3] -sum(log((1+x)*(1+be*x)*teˆ2+al*be*(1+te+te*x))-log(te+1)-(al+1) *log(1+be*x)-te*x)} est=nlm(logL,c(1,.01,.01)) alpha=est $estimate…”

Estimation and Prediction for the Power-Exponential Hazard Rate Distribution Based on Record Data

“…Unfortunately, these hazard rate functions are monotone and therefore they do not provide a reasonable parametric fit for modeling phenomenon with bathtubshaped hazard rates which are common in biological and reliability studies. Recently, Tarvirdizade and Nematollahi (2019) introduced a more general hazard rate function by combining the power hazard rate function and the exponential hazard rate function. This is the power-exponential hazard rate function, defined as…”

“…The exponential, Rayleigh, Weibull, modified Weibull, Gompertz, Gompertz-Makeham, linear hazard rate and power hazard rate distributions are the most important sub-models of the P-EHRD. Some distributional properties and estimation of the parameters based on a complete sample for the P-EHRD were studied by Tarvirdizade and Nematollahi (2019). They have also showed that the P-EHRD provides a better fit than other four-parameter distributions for data with a bathtub-shaped hazard rate while its hazard rate function is very simple in comparison with those of the competitor distributions.…”