In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is as...In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.展开更多
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...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.展开更多
Three-parameter Weibull distribution is one of the preferable distribution models to describe product life. However, it is difficult to estimate its location parameter in the situation of a small size of sample. This ...Three-parameter Weibull distribution is one of the preferable distribution models to describe product life. However, it is difficult to estimate its location parameter in the situation of a small size of sample. This paper presents a stochastic simulation method to estimate the Weibull location parameters according to a small size of sample of product life observations and a large amount of statistically simulated life date. Big data technique is applied to find the relationship between the minimal observation in a product life sample of size <em>n</em> (<em>n</em> ≥ 3) and the Weibull location parameter. An example is presented to demonstrate the applicability and the value of the big data based stochastic simulation method. Comparing with other methods, the stochastic simulation method can be applied to very small size of sample such as the sample size of three, and it is easy to apply.展开更多
基金Supported by the National Natural Science Foundation of China(11671375 and 11471303)Natural Science Foundation of Anhui Provincial Education Department(KJ2017A171)
文摘In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.
文摘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.
文摘Three-parameter Weibull distribution is one of the preferable distribution models to describe product life. However, it is difficult to estimate its location parameter in the situation of a small size of sample. This paper presents a stochastic simulation method to estimate the Weibull location parameters according to a small size of sample of product life observations and a large amount of statistically simulated life date. Big data technique is applied to find the relationship between the minimal observation in a product life sample of size <em>n</em> (<em>n</em> ≥ 3) and the Weibull location parameter. An example is presented to demonstrate the applicability and the value of the big data based stochastic simulation method. Comparing with other methods, the stochastic simulation method can be applied to very small size of sample such as the sample size of three, and it is easy to apply.
