Truncated Length-Biased Power Garima Distribution: Properties and Application

A new distribution for lifetime data, called the truncated length-biased power Garima (TLBPG) distribution was developed as a truncation of the length-biased power Garima (LBPG) distribution, including the truncated length-biased Garima (TLBG) distribution as a special case. Some properties of the TLBPG distribution such as moments, survival function and hazard rate function were derived, while parameters of the TLBPG distribution were estimated by the maximum likelihood (ML) method. A simulation study was applied to illustrate the efficiency of model parameter estimation, using the ML method based on the mean square error of estimates. The simulation study results showed that the ML estimates had high efficiency when the sample size was large. The TLBPG distribution was also applied to real data sets, with performance compared to other existing distributions (e.g., the TLBG, LBPG and length-biased Garima distributions). Based on the Kolmogorov–Smirnov and Cramer–von Mises tests, results showed that the TLBPG distribution described the data sets better than the TLBG, LBPG, truncated Lindley, truncated two-parameter Lindley and length-biased Garima distributions.