Estimation of Parameters of Truncated or Censored Exponential Distributions
Open accessAbstract
This paper gives maximum likelihood estimators of parameters of truncated and censored exponential distributions, asymptotic variances of the estimators, and asymptotic confidence intervals for the parameters. Applications to bombing accuracy studies and to life testing are pointed out. As regards bombing accuracy the parameter estimated is the reciprocal of the variance in a normal bivariate distribution having circular symmetry. The reciprocal is estimated because there is no maximum likelihood estimator of the variance and any estimator of the variance is badly biased (see Section 2). Results of a synthetic sampling experiment are given to provide information on rapidity of convergence of the distributions of the estimators to their asymptotic distributions.
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Unknown distances can be imputed using the ultrametric inequality by finding the minimum over intermediate populations of the maximum of the two known distances.
“Using the ultrametric inequality, we can impute unknown distances d(i,j) simply by searching across all intermediate populations k and finding the minimum103, mink∈pops{max{di,k,dj,k}}.”
From Paths and timings of the peopling of Polynesia inferred from genomic networks (2021) · cites this paper as [103]
The Summary (p. 1) describes estimation for truncated and censored exponential distributions, and the Maximum-likelihood estimators section (pp. 2–3) develops those estimators. Searches for the ultrametric inequality and for imputing population distances through an intermediate population found no passage addressing the claimed method. (LLM, conf=0.75)
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Cites
Statistical Theory with Engineering Applications
Hald, A., & Friedman, B. (1953) · Physics Today · doi:10.1063/1.3061079 · Cited by 1,537 · see citing works
Introduction to the Theory of Statistics.
Wolfowitz, J., & Mood, A. M. (1951) · American Mathematical Monthly · doi:10.2307/2307742 · Cited by 543 · see citing works
Some Theorems Relevant to Life Testing from an Exponential Distribution
Epstein, B., & Sobel, M. (1954) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728793 · Cited by 319 · see citing works
Maximum Likelihood Estimation in Truncated Samples
Halperin, M. (1952) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729439 · Cited by 120 · see citing works
Estimation of the variance of the bivariate normal distribution
Hughes, H. M. (1949) · Medical Entomology and Zoology · Cited by 4 · see citing works
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Paths and timings of the peopling of Polynesia inferred from genomic networks
Ioannidis, A. G., Blanco-Portillo, J., Sandoval, K., Hagelberg, E., Barberena-Jonas, C., Hill, A. V. S., Rodríguez-Rodríguez, J. E., Fox, K., Robson, K., Haoa-Cardinali, S., et al. (2021) · Nature · doi:10.1038/s41586-021-03902-8 · Cited by 124 · see citing works
- Authors
- Deemer, W. L., & Votaw, D. F.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1955-09
- Volume
- 26
- Issue
- 3
- Pages
- 498-504
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2087061824
- Semantic Scholar
- 84425d76366c8aeede227f68a8209fc34b9dfece
- Cited by
- 102
- References
- 5
- Citations by year
- 2024: 2 · 2023: 4 · 2022: 1 · 2021: 3 · 2019: 1 · 2017: 2 · 2016: 7 · 2015: 2 · 2014: 5 · 2013: 1 · 2012: 5
- FWCI
- 1.71
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Mathematical Statistics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- truncated exponential distribution, maximum likelihood estimation, asymptotic variance, asymptotic confidence intervals, life testing, estimation bias
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