Maximum-Likelihood Estimation of the Parameters of Gamma and Weibull Populations from Complete and from Censored Samples

Harter, H. Leon; Moore, Albert H.

doi:10.1080/00401706.1965.10490304

Cited by 170 publications

(52 citation statements)

References 7 publications

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“…To obtain Maximum Likelihood estimators, iterative methods are required (e.g., Harter and Moore, 1965;Bain and Antle, 1967;Ek et al, 1975). In the present study, the LIFEREG procedure in SAS/STAT TM (SAS Institute Inc., 2003) was used to calculate parameters b and c of the Weibull distribution.…”

Section: -Maximum Likelihood (Ml)mentioning

confidence: 99%

A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiate and Pinus sylvestris stands in northwest Spain

Gorgoso¹,

Rojo

Cámara-Obregón

et al. 2012

For. syst.

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The purpose of this study was to compare the accuracy of the Weibull, Johnson's S B and beta distributions, fitted with some of the most usual methods and with different fixed values for the location parameters, for describing diameter distributions in even-aged stands of Pinus pinaster, Pinus radiata and Pinus sylvestris in northwest Spain. A total of 155 permanent plots in Pinus sylvestris stands throughout Galicia, 183 plots in Pinus pinaster stands throughout Galicia and Asturias and 325 plots in Pinus radiata stands in both regions were measured to describe the diameter distributions. Parameters of the Weibull function were estimated by Moments and Maximum Likelihood approaches, those of Johnson's S B function by Conditional Maximum Likelihood and by Knoebel and Burkhart's method, and those of the beta function with the method based on the moments of the distribution.The beta and the Johnson's S B functions were slightly superior to Weibull function for Pinus pinaster stands; the Johnson's S B and beta functions were more accurate in the best fits for Pinus radiata stands, and the best results of the Weibull and the Johnson's S B functions were slightly superior to beta function for Pinus sylvestris stands. However, the three functions are suitable for this stands with an appropriate value of the location parameter and estimation of parameters method.

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Section: -Maximum Likelihood (Ml)mentioning

confidence: 99%

A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiate and Pinus sylvestris stands in northwest Spain

Gorgoso¹,

Rojo

Cámara-Obregón

et al. 2012

For. syst.

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“…These three are similar in that the two-parameter versions have positive density only if x > 0, while the three-parameter versions allow for a shifted origin so that the density is positive only for x > a. In their three-parameter versions, the lognormal model was investigated by Cohen (1951), Hill (1963), and Harter and Moore (1966), among others; the gamma model by Harter and Moore (1965) and Cohen and Norgaard (1977); the Weibull model by Harter and Moore (1965), Dubey (1966), and Rockette, Antle, and Klimko (1974).…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, for a given sample there may be no local maximum. Thus the technique is not foolproof and it has to be augmented by additional ad hoc methods (see Harter and Moore 1966).…”

Section: Introductionmentioning

confidence: 99%

Maximum Likelihood Estimation of Parameters in the Inverse Gaussian Distribution, with Unknown Origin

Cheng¹,

Amin²

1981

Technometrics

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“…However, it does not seem justified to assume the duration of latency (X2) is exponentially distributed. An alternative worthy of consideration might be the three parameter gamma density (see, for example, Harter & Moore, 1965). For present purposes a normal approximation is chosen to avoid considerable calculation.…”

Section: Methodsmentioning

confidence: 99%

Estimating the duration of latency and survival time of snails with schistosomiasis

Goddard

1979

J. Hyg.

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By means of techniques of analyses of survival data developed for cancer trials it is possible to study aspects of the natural history of the infection of schistosomiasis on the intermediate host of transmission, the snail.The simultaneous study of three response variables is largely based on a model of Lagakos (1976). When using this approach in the schistosomiasis setting it seems inappropriate to assume that one process, the duration of latency, follows an exponential distribution. Thus this stage is modified to follow a normal distribution and the derivatives required to obtain maximum-likelihood estimates and approximate variances of all parameters are provided.Simple graphical tools for assessing the validity of distributional assumptions in survival data are available from industrial research. The reader's attention is drawn to a paper by Nelson (1972). The relevance and application of these methods to the current problem are described in Section 4.In the event that the times to death of prepatent and patent snails do not follow exponential distributions as assumed in the primary model, a further modification is introduced to enable either or both to follow Weibull densities.Lastly it is possible to adapt both the primary model of Section Three and the modified model of Section Five to allow for the inclusion of auxiliary variables or covariates. Again the required derivatives to obtain maximum likelihood estimates and approximate variances are provided.I wish to thank Sheila Gore, Stuart Pocock and Professor Michael Healy for many useful discussions. Sheila Gore and Professor Peter Armitage provided many recommendations for the improvement of the manuscript for which I am most grateful.

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Maximum-Likelihood Estimation of the Parameters of Gamma and Weibull Populations from Complete and from Censored Samples

Cited by 170 publications

References 7 publications

A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiate and Pinus sylvestris stands in northwest Spain

A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiate and Pinus sylvestris stands in northwest Spain

Maximum Likelihood Estimation of Parameters in the Inverse Gaussian Distribution, with Unknown Origin

Estimating the duration of latency and survival time of snails with schistosomiasis

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