Multi - sample test of equal gamma distribution scale parameters in presence of unknown common shape parameter

1992 ◽  
Vol 21 (6) ◽  
pp. 1633-1650 ◽  
Author(s):  
S.R. Paul ◽  
K. Thiagarajah
Keyword(s):  
Gamma Distribution ◽  
Shape Parameter ◽  
Scale Parameters ◽  
Sample Test ◽  
Common Shape

scholarly journals Statistical Downscaling of Daily Wind Speed Variations

2014 ◽  
Vol 53 (3) ◽  
pp. 660-675 ◽  
Author(s):  
Megan C. Kirchmeier ◽  
David J. Lorenz ◽  
Daniel J. Vimont
Keyword(s):  
Wind Speed ◽  
Gamma Distribution ◽  
Large Scale ◽  
Probabilistic Method ◽  
Probabilistic Approach ◽  
Local Scale ◽  
Scale Parameters ◽  
Wind Speeds ◽  
Distribution Shape ◽  
Realistic Information

AbstractThis study presents the development of a method to statistically downscale daily wind speed variations in an extended Great Lakes region. A probabilistic approach is used, predicting a daily-varying probability density function (PDF) of local-scale daily wind speed conditioned on large-scale daily wind speed predictors. Advantages of a probabilistic method are that it provides realistic information on the variance and extremes in addition to information on the mean, it allows the autocorrelation of downscaled realizations to be tuned to match the autocorrelation of local-scale observations, and it allows flexibility in the use of the final downscaled product. Much attention is given to fitting the proper functional form of the PDF by investigating the observed local-scale wind speed distribution (predictand) as a function of the decile of the large-scale wind (predictor). It is found that the local-scale standard deviation and the local-scale shape parameter (from a gamma distribution) are nonconstant functions of the large-scale predictor. As such, a vector generalized linear model is developed to relate the large-scale and local-scale wind speeds. Maximum likelihood and cross validation are used to fit local-scale gamma distribution shape and scale parameters to the large-scale wind speed. The result is a daily-varying probability distribution of local-scale wind speed, conditioned on the large-scale wind speed.

On the quantiles of the gamma and F distributions

1978 ◽  
Vol 15 (2) ◽  
pp. 426-432 ◽  
Author(s):  
I. W. Saunders ◽  
P. A. P. Moran
Keyword(s):  
Gamma Distribution ◽  
Shape Parameter

We show, in the context of a neurobiological problem, that ζ a(α)−ζ a(β) increases with a, while ζ a (α)/ζ a (β) decreases with a, where 0 < β < α < 1 and ζ a (α) is the α th quantile of either the gamma distribution with shape parameter a, or a scaled F distribution with parameters 2a and 2m for any m.

scholarly journals Distribution of Myosin Attachment Times Predicted from Viscoelastic Mechanics of Striated Muscle

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Bradley M. Palmer ◽  
Yuan Wang ◽  
Mark S. Miller
Keyword(s):  
Exponential Distribution ◽  
Gamma Distribution ◽  
Shape Parameter ◽  
Striated Muscle ◽  
Scale Parameter ◽  
Viscoelastic Model ◽  
A Value ◽  
Temporal Events ◽  
Single Exponential

We demonstrate that viscoelastic mechanics of striated muscle, measured as elastic and viscous moduli, emerge directly from the myosin crossbridge attachment time,tatt, also called time-on. The distribution oftattwas modeled using a gamma distribution with shape parameter,p, and scale parameter,β. At 5 mM MgATP,βwas similar between mouseα-MyHC (16.0±3.7 ms) andβ-MyHC (17.9±2.0 ms), andpwas higher (P<0.05) forβ-MyHC (5.6±0.4no units) compared toα-MyHC (3.2±0.9). At 1 mM MgATP,papproached a value of 10 in both isoforms, butβrose only in theβ-MyHC (34.8±5.8 ms). The estimated meantatt(i.e.,pβproduct) was longer in theβ-MyHC compared toα-MyHC, and became prolonged in both isoforms as MgATP was reduced as expected. The application of our viscoelastic model to these isoforms and varying MgATP conditions suggest thattattis better modeled as a gamma distribution due to its representing multiple temporal events occurring withintattcompared to a single exponential distribution which assumes only one temporal event withintatt.

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