m******t
发帖数: 273 | 1 I need to estimate a truncated gamma distribution paramters (shape , scale).
But, I only know the data mean and std. dev. I do not know the dat set.
Given the mean and std. dev. of a data set from a trucnated gamma
distribution, how to find shape and scale of the distribution parameters ?
I know MLE may be sueful for solving this problem. But, they depend on
knowing the whole data set.
Any help would be appreciated. | I*****a
发帖数: 5425 | 2 这个不能吧
).
【在 m******t 的大作中提到】
: I need to estimate a truncated gamma distribution paramters (shape , scale).
: But, I only know the data mean and std. dev. I do not know the dat set.
: Given the mean and std. dev. of a data set from a trucnated gamma
: distribution, how to find shape and scale of the distribution parameters ?
: I know MLE may be sueful for solving this problem. But, they depend on
: knowing the whole data set.
: Any help would be appreciated.
| m******t
发帖数: 273 | 3 why ?
Any help would be appreciated !
【在 I*****a 的大作中提到】
: 这个不能吧
:
: ).
| c********h
发帖数: 330 | 4 没有算过truncated gamma的mle，可以表示成mean和std的函数吗？
要是可以就结了
我猜是没戏，一般location的mle都是什么最大最小统计量吧 | I*****a
发帖数: 5425 | 5 你是只有两个值mean 和sd 吗？
但是你parameters 不是有三个吗？
【在 m******t 的大作中提到】
: why ?
: Any help would be appreciated !
| m******t
发帖数: 273 | 6 Yes, I have only mean and std. dev.
I only need to find shape, scale. If we can also find location, it will be
better.
I have a group of data mean and std. dev. It means that each data point in
the given set is a mean and std. dev., which are calculated from a truncated
gamma distribution.
Each point may have a different truncated gamma distribution, which has the
same truncated values.
They may have some relationship between any two data point (mean, std.dev.),
but, we do not know.
So, it makes no sense to calculate the mean and std. dev. of the data set.
Thanks !
【在 I*****a 的大作中提到】
: 你是只有两个值mean 和sd 吗？
: 但是你parameters 不是有三个吗？
| s******u
发帖数: 21 | 7 你试下 method of moment 吧， 看看 shape 和scale 和 mean ,variance 有没有啥
关系，然后反解 得到shaple 和 scale~~ 如果能做到这一步的话，可以再用
parametric bootstrap (用估计得到 shape 和 scale当成真实的) 得到 估计值的方差
).
【在 m******t 的大作中提到】
: I need to estimate a truncated gamma distribution paramters (shape , scale).
: But, I only know the data mean and std. dev. I do not know the dat set.
: Given the mean and std. dev. of a data set from a trucnated gamma
: distribution, how to find shape and scale of the distribution parameters ?
: I know MLE may be sueful for solving this problem. But, they depend on
: knowing the whole data set.
: Any help would be appreciated.
| R*****0
发帖数: 146 | 8 First let's start with original Gamma distribution.
MLE: It is not hard to see the sufficient statistics are the 'mean' and the
'mean of log(data)'. The MLE for shape is accessible using Newton method.
Moment Method: Quite straightforward -> mean = shape*scale, var = shape*(
scale)^2.
However, truncated Gamma, if I get it, is much difficult even if you know
the interval [a,b] for truncation. The density function will have the form g
(x;shape,scale)/[G(b;shape,scale)-G(a;shape,scale)] on [a,b]. Since the
denominator involves incomplete Gamma integral with both parameters, either
MLE or MME will be hard to obtain. Note that it is still true that the 'mean
' and the 'mean of log(data)' are sufficient.
But you may google your concern. I believe someone has already got something
. | m******t
发帖数: 273 | 9 Thanks for all your help.
I have tried Moment Method, but the QQ-plot result is very bad.
How to know that truncated gamma pdf is the form of ?
g(x;shape,scale)/[G(b;shape,scale)-G(a;shape,scale)] on [a,b].
Are there some papers about that ?
'mean of log(data)' is unknown. We only know mean of data.
From, http://en.wikipedia.org/wiki/Gamma_distribution
If ln(x_i) is known, I can get estimated shape parameter. But, it is unknown
.
Any help would be appreciated.
First let's start with original Gamma distribution.
MLE: It is not hard to see the sufficient statistics are the 'mean' and the
'mean of log(data)'. The MLE for shape is accessible using Newton method.
Moment Method: Quite straightforward -> mean = shape*scale, var = shape*(
scale)^2.
However, truncated Gamma, if I get it, is much difficult even if you know
the interval [a,b] for truncation. The density function will have the form g
(x;shape,scale)/[G(b;shape,scale)-G(a;shape,scale)] on [a,b]. Since the
denominator involves incomplete Gamma integral with both parameters, either
MLE or MME will be hard to obtain. Note that it is still true that the 'mean
' and the 'mean of log(data)' are sufficient.
But you may google your concern. I believe someone has already got something
【在 R*****0 的大作中提到】
: First let's start with original Gamma distribution.
: MLE: It is not hard to see the sufficient statistics are the 'mean' and the
: 'mean of log(data)'. The MLE for shape is accessible using Newton method.
: Moment Method: Quite straightforward -> mean = shape*scale, var = shape*(
: scale)^2.
: However, truncated Gamma, if I get it, is much difficult even if you know
: the interval [a,b] for truncation. The density function will have the form g
: (x;shape,scale)/[G(b;shape,scale)-G(a;shape,scale)] on [a,b]. Since the
: denominator involves incomplete Gamma integral with both parameters, either
: MLE or MME will be hard to obtain. Note that it is still true that the 'mean
| c*******1
发帖数: 240 | 10 quick and dirty:
用monte carlo 算mle，只要电脑快就行。 |
|
