Abstract
In this paper, we use the lower record values from the inverse Weibull distribution (IWD) to develop and discuss different methods of estimation in two different cases, 1) when the shape parameter is known and 2) when both of the shape and scale parameters are unknown. First, we derive the best linear unbiased estimate (BLUE) of the scale parameter of the IWD. To compare the different methods of estimation, we present the results of Sultan (2007) for calculating the best linear unbiased estimates (BLUEs) of the location and scale parameters of IWD. Second, we derive the maximum likelihood estimates (MLEs) of the location and scale parameters. Further, we discuss some properties of the MLEs of the location and scale parameters. To compare the different estimates we calculate the relative efficiency between the obtained estimates. Finally, we propose some numerical illustrations by using Monte Carlo simulations and apply the findings of the paper to some simulated data.
Highlights
Record values arise naturally in many real life applications involving data relating to weather, sport, economics and life testing studies
To compare the different methods of estimation, we present the results of Sultan (2007) for calculating the best linear unbiased estimates (BLUEs) of the location and scale parameters of IWD
[11] have discussed some inferential methods based on record values from Gumbel distribution. [12,13] have discussed inferential techniques based on Weibull and generalized Pareto distributions, respectively
Summary
Record values arise naturally in many real life applications involving data relating to weather, sport, economics and life testing studies. Reference [8] has established some recurrence relations for the moments of record values from the Gumbel distribution. Reference [11] have discussed some inferential methods based on record values from Gumbel distribution. [12,13] have discussed inferential techniques based on Weibull and generalized Pareto distributions, respectively. Reference [14] have compared different estimates based on record values from Weibull distribution. Reference [15] has considered different loss functions to develop the Bayesian estimates of the parameters of the IWD. The joint density function of the first n lower record values X L(1) , X L(2) , , X L(n) is given by [5].
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