加權極大似然估計求參數命令

『壹』 求助高手matlab的極大似然估計問題（mle）求解

[phat,pci] = mle(data,'lognormal');
data 是這一組數據，'lognormal'的意思是對數正態分布，phat 為參數， pci是一個上界和一個下界，是phat的95%的置信區間

『貳』 急求matlab用極大似然估計求解威布爾估計的兩個參數的步驟及代碼（有注釋最好），謝謝

[phat,pci] = mle(data,'lognormal');
data 是這一組數據,'lognormal'的意思是對數正態分布,phat 為參數,pci是一個上界和一個下界,是phat的95%的置信區間！

『叄』 二項分布的極大似然估計怎麼求

二項分布就是n個兩點分布，兩點分布的概率是P=p^x*(1-p)^(1-x)，所以似然函數 L=p^∑Xi*（1-p）^(n-∑Xi)，構造 lnL=∑Xi*lnp+(n-∑Xi) ln(1-p)，對p進行求導，令其結果等於0，就是∑Xi/p+(n-∑Xi)/(1-p)=0，通分後令分母等於0，可以得到p=（∑Xi）/n

求極大似然函數估計值的一般步驟：

（1） 寫出似然函數；

（2） 對似然函數取對數，並整理；

（3） 求導數；

（4） 解似然方程 。

(3)加權極大似然估計求參數命令擴展閱讀：

極大似然估計只是一種粗略的數學期望，要知道它的誤差大小還要做區間估計。極大似然估計是建立在這樣的思想上：已知某個參數能使這個樣本出現的概率最大，我們當然不會再去選擇其他小概率的樣本，所以乾脆就把這個參數作為估計的真實值。

極大似然估計，只是一種概率論在統計學的應用，它是參數估計的方法之一。說的是已知某個隨機樣本滿足某種概率分布，但是其中具體的參數不清楚，參數估計就是通過若干次試驗，觀察其結果，利用結果推出參數的大概值。

『肆』 極大似然估計求出廣義極值分布中的參數在sas中怎麼實現

proc genmod data = eyestudy;
class carrot id;
model lenses = carrot/ dist = poisson link = log;
repeated subject = id/ type = unstr;
estimate 'Beta' carrot 1 -1/ exp;*此步驟輸出RR值;
run;

『伍』 極大似然估計中參數標准差怎麼估計

L(θ,c)=∏f(xi)(i=1,2,…,n)(x>=c)

然後對取L(θ,c)的對數，再對L(θ,c)求分別求偏導，令它=0，即可得出θ,c與x1,x2,…,xn的關系，根據實際意義選取合適的值；下面是具體步驟：

1. 先寫出L(θ,c)=f(x1)*f(x2)…f(xn)

2. Ln(L)=-nLnθ-(1/θ)(∑xi-nc)

3. 2.對c求偏導=n/θ>0;

4. 而由題意有x>=c,所以c的極大似然估計量為min(x1,x2,…,xn)

5. 3.對θ求偏導,=-(n/θ)+(1/θ^2)(∑xi-nc)

6. 令它=0,所以θ=(1/n)(∑xi)-c

7. 4.綜合上面所述，所以c的極大似然估計量為min(xi)

8. θ的極大似然估計量為(1/n)(∑xi)-min(xi)
   

『陸』 設總體 的密度函數f(x)=(a+1)*x^a,0<x<1 試分別用矩估計法和極大似然估計法求參數 a的估計。

解題過程如下圖：

(6)加權極大似然估計求參數命令擴展閱讀

如果概率密度函數fX(x)在一點x上連續，那麼累積分布函數可導。

由於隨機變數X的取值 只取決於概率密度函數的積分，所以概率密度函數在個別點上的取值並不會影響隨機變數的表現。更准確來說，如果一個函數和X的概率密度函數取值不同的點只有有限個、可數無限個或者相對於整個實數軸來說測度為0（是一個零測集），那麼這個函數也可以是X的概率密度函數。

連續型的隨機變數取值在任意一點的概率都是0。作為推論，連續型隨機變數在區間上取值的概率與這個區間是開區間還是閉區間無關。要注意的是，概率P{x=a}=0，但{X=a}並不是不可能事件。

『柒』 請問，如果利用最大似然法求模型參數（在MATLAB中）

有啊，看幫助文件吧。
>>help mle
MLE Maximum likelihood estimation.
PHAT = MLE(DATA) returns maximum likelihood estimates (MLEs) for the
parameters of a normal distribution, computed using the sample data in
the vector DATA.

[PHAT, PCI] = MLE(DATA) returns MLEs and 95% confidence intervals for
the parameters.

[...] = MLE(DATA,'distribution',DIST) computes parameter estimates for
the distribution specified by DIST. DIST is a character string
containing the name of one of the distributions supported by MLE.

[...] = MLE(DATA, ..., 'NAME1',VALUE1,'NAME2',VALUE2,...) specifies
optional argument name/value pairs chosen from the following list.
Argument names are case insensitive and partial matches are allowed.

Name Value
'censoring' A boolean vector of the same size as DATA,
containing ones when the corresponding elements of
DATA are right-censored observations and zeros when
the corresponding elements are exact observations.
Default is all observations observed exactly.
Censoring is not supported for all distributions.
'frequency' A vector of the same size as DATA, containing
non-negative integer frequencies for the corresponding
elements in DATA. Default is one observation per
element of DATA.
'alpha' A value between 0 and 1 specifying a confidence level
of 100*(1-alpha)% for PCI. Default is alpha=0.05 for
95% confidence.
'ntrials' A scalar, or a vector of the same size as DATA,
containing the total number of trials for the
corresponding element of DATA. Applies only to the
binomial distribution.
'options' A structure created by a call to STATSET, containing
numerical options for the fitting algorithm. Not
applicable to all distributions.

MLE can also fit a custom distribution that you define using
distribution functions, in one of three ways:

[...] = MLE(DATA,'pdf',PDF,'cdf',CDF,'start',START,...) returns MLEs
for the parameters of the distribution defined by the probability
density and cumulative distribution functions PDF and CDF. PDF and CDF
are function handles created using @. They accept as inputs a vector
of data and one or more indivial distribution parameters, and return
vectors of probability density values and cumulative probability
values, respectively. If the 'censoring' name/value pair is not
present, you may omit the 'cdf' name/value pair. MLE computes the
estimates by numerically maximizing the distribution's log-likelihood,
and START is a vector containing initial values for the parameters.

[...] = MLE(DATA,'logpdf',LOGPDF,'logsf',LOGSF,'start',START,...)
returns MLEs for the parameters of the distribution defined by the log
probability density and log survival functions LOGPDF and LOGSF. LOGPDF
and LOGSF are function handles created using @. They accept as inputs
a vector of data and one or more indivial distribution parameters,
and return vectors of logged probability density values and logged
survival function values, respectively. This form is sometimes more
robust to the choice of starting point than using PDF and CDF
functions. If the 'censoring' name/value pair is not present, you may
omit the 'logsf' name/value pair. START is a vector containing initial
values for the distribution's parameters.

[...] = MLE(DATA,'nloglf',NLOGLF,'start',START,...) returns MLEs for
the parameters of the distribution whose negative log-likelihood is
given by NLOGLF. NLOGLF is a function handle specified using @, that
accepts the four input arguments
PARAMS - a vector of distribution parameter values
DATA - a vector of data
CENS - a boolean vector of censoring values
FREQ - a vector of integer data frequencies
NLOGLF must accept all four arguments even if you do not supply the
'censoring' or 'frequency' name/value pairs (see above). However,
NLOGLF can safely ignore its CENS and FREQ arguments in that case.
NLOGLF returns a scalar negative log-likelihood value and, optionally,
a negative log-likelihood gradient vector (see the 'GradObj' STATSET
parameter below). START is a vector containing initial values
for the distribution's parameters.

PDF, CDF, LOGPDF, LOGSF, or NLOGLF can also be cell arrays whose first
element is a function handle as defined above, and whose remaining
elements are additional arguments to the function. MLE places these
arguments at the end of the argument list in the function call.

The following optional argument name/value pairs are valid only when
'pdf' and 'cdf', 'logpdf' and 'logcdf', or 'nloglf' are given.

'lowerbound' A vector the same size as START containing lower bounds
for the distribution parameters. Default is -Inf.
'upperbound' A vector the same size as START containing upper bounds
for the distribution parameters. Default is Inf.
'optimfun' A string, either 'fminsearch' or 'fmincon', naming the
optimization function to be used in maximizing the
likelihood. Default is 'fminsearch'. You may only
specify 'fmincon' if the Optimization Toolbox is
available.

When fitting a custom distribution, use the 'options' parameter to
control details of the maximum likelihood optimization. See
STATSET('mlecustom') for parameter names and default values. MLE
interprets the following STATSET parameters for custom distribution
fitting as follows:

'GradObj' 'on' or 'off', indicating whether or not FMINCON
can expect the function provided with the 'nloglf'
name/value pair to return the gradient vector of the
negative log-likelihood as a second output. Default
is 'off'. Ignored when using FMINSEARCH.
'DerivStep' The relative difference used in finite difference
derivative approximations when using FMINCON, and
'GradObj' is 'off'. May be a scalar, or the same
size as START. EPS^(1/3) by default. Ignored when
using FMINSEARCH.
'FunValCheck' 'on' or 'off', indicating whether or not MLE should
check the values returned by the custom distribution
functions for validity. Default is 'on'. A poor
choice of starting point can sometimes cause these
functions to return NaNs, infinite values, or out of
range values if they are written without suitable
error-checking.
'TolBnd' An offset for upper and lower bounds when using
FMINCON. MLE treats upper and lower bounds as
strict inequalities (i.e., open bounds). With
FMINCON, this is approximated by creating closed
bounds inset from the specified upper and lower
bounds by TolBnd. Default is 1e-6.

『捌』 求參數的極大似然估計（要詳細步驟）謝謝