Modified maximum likelihood estimation for rayleigh distribution

Lalitha, S.; Mishra, Anand

doi:10.1080/03610929608831702

Cited by 46 publications

(30 citation statements)

References 5 publications

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“…We used the computer program distfit from the Theseus package (Theobald and Wuttke, 2006) to test 20 different distributions and selected the Rayleigh distribution as the most appropriate according to the Bayesian information criterion. The Rayleigh distribution (Lalitha and Mishra, 1996) is characterized by a single parameter, λ which indicates the maximum (mode) of the distribution:

R (x; λ) = \frac{x}{λ^{2}} e^{- x^{2} / 2 λ^{2}} .

…”

Section: Methodsmentioning

confidence: 99%

Beam-induced motion of vitrified specimen on holey carbon film

Brilot

Chen

Cheng

et al. 2012

Journal of Structural Biology

385

337

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The contrast observed in images of frozen-hydrated biological specimens prepared for electron cryo-microscopy falls significantly short of theoretical predictions. In addition to limits imposed by the current instrumentation, it is widely acknowledged that motion of the specimen during its exposure to the electron beam leads to significant blurring in the recorded images. We have studied the amount and direction of motion of virus particles suspended in thin vitrified ice layers across holes in perforated carbon films using exposure series. Our data show that the particle motion is correlated within patches of 0.3 – 0.5 μm, indicating that the whole ice layer is moving in a drum-like motion, with accompanying particle rotations of up to a few degrees. Support films with smaller holes, as well as lower electron dose rates tend to reduce beam-induced specimen motion, consistent with a mechanical effect. Finally, analysis of movies showing changes in the specimen during beam exposure show that the specimen moves significantly more at the start of an exposure than towards its end. We show how alignment and averaging of movie frames can be used to restore high-resolution detail in images affected by beam-induced motion.

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R (x; λ) = \frac{x}{λ^{2}} e^{- x^{2} / 2 λ^{2}} .

…”

Section: Methodsmentioning

confidence: 99%

Beam-induced motion of vitrified specimen on holey carbon film

Brilot

Chen

Cheng

et al. 2012

Journal of Structural Biology

385

337

View full text Add to dashboard Cite

show abstract

“…Likewise, the distribution of wave heights and crests might be Rayleigh (Tayfuna and Fedeleb 2007). Other aspects of this model are treated in Sinha and Howlader (1983);Howlader (1985); Aminzadeh (1991); Lalitha and Mishra (1996); Fernández (2000); Aslam (2007); Dey and Das (2007) and Liang (2007).…”

Section: Rayleigh Distribution: Applications and Likelihoodmentioning

confidence: 98%

Bayesian estimation and prediction based on Rayleigh sample quantiles

Fernández

2009

Qual Quant

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“…Iwase & Kanefuji [16] studied the modified maximum likelihood estimators and modified moment estimators for the Log-normal distribution with shifted unknown origin. Lalitha & Mishra [17] suggested the modified maximum-likelihood estimation for scale-parameter of the Rayleigh distribution. Modifications in maximum likelihood estimation and method moments have also been found better than traditional estimators for two-parameter Exponential distribution [18].…”

Section: Maximum Likelihood Estimation Is Considered As Most Importanmentioning

confidence: 99%