Comparison of Lower Bounds for the Variance of Unbiased Estimators for some Well-known Families of Distributions
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S. Nayeban
Abstract
One of the most fundamental issues in estimation theory about accuracy of an unbiased estimator is computing or approximating its variance. Very often, the variance has a complicated form or cannot be computed explicitly. In this paper, we consider two well-known lower bounds for the variance of unbiased estimator, namely the Bhattacharyya (1946, 1947) and the Kshirsagar (2000) bounds for some versatile families of distributions in statistics and especially in reliability analysis. We consider the generalized gamma (GG), inverse Gaussian, Burr type XII and Burr type III distributions, and derive for these distributions, general forms of Bhattacharyya and Kshirsagar matrices. Additionally, we evaluate different Bhattacharyya and Kshirsagar bounds for the variance of estimators of some functions of relevant parameters and arrive at proposal which of the bounds should be used in given situations.
©2014 Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Assessment of Traditional Demerits and a New Ordinal Alternative
- Acceptance Sampling Plans Under Truncated Life Tests Assuming a Half Exponential Power Life Distribution
- Comparison of Lower Bounds for the Variance of Unbiased Estimators for some Well-known Families of Distributions
- Order k Version of the Alternative Hyper-Poisson Distribution
- Marshall–Olkin Morgenstern–Weibull distribution: generalisations and applications
- X̅ Charts with Variable Control and Warning Limits
- Transmuted Generalized Inverted Exponential Distribution
- Selection of modified quick switching systems for given acceptable and limiting quality levels with minimum risks using weighted poisson distribution
- Multivariate Process Capability Index: A Review and Some Results
- Selection of Bayesian Single Sampling Plans by Attributes with Desired Discrimination
Articles in the same Issue
- Frontmatter
- Assessment of Traditional Demerits and a New Ordinal Alternative
- Acceptance Sampling Plans Under Truncated Life Tests Assuming a Half Exponential Power Life Distribution
- Comparison of Lower Bounds for the Variance of Unbiased Estimators for some Well-known Families of Distributions
- Order k Version of the Alternative Hyper-Poisson Distribution
- Marshall–Olkin Morgenstern–Weibull distribution: generalisations and applications
- X̅ Charts with Variable Control and Warning Limits
- Transmuted Generalized Inverted Exponential Distribution
- Selection of modified quick switching systems for given acceptable and limiting quality levels with minimum risks using weighted poisson distribution
- Multivariate Process Capability Index: A Review and Some Results
- Selection of Bayesian Single Sampling Plans by Attributes with Desired Discrimination
