1、1MATLAB 程序設計程序設計Department of Civil EngineeringHefei University of Technology 第九章 概率與統計分析2本章內容： 統計分布的數字特征 樣本分布的頻數直方圖描述 概率函數、分布函數、逆分布函數和隨機數的發生第三章 概率與統計分析31. 統計分布的數字特征第三章 概率與統計分析41. 統計分布的數字特征平均值：平均值：mean Average or mean value of arraySyntaxM = mean(A)M = mean(A,dim)DescriptionM = mean(A) returns the m

2、ean values of the elements along different dimensions of an array. If A is a vector, mean(A) returns the mean value of A.If A is a matrix, mean(A) treats the columns of A as vectors, returning a row vector of mean values. 第三章 概率與統計分析5第三章 概率與統計分析61. 統計分布的數字特征中值：中值：medianMedian value of arraySyntaxM =

3、 median(A)M = median(A,dim)DescriptionM = median(A) returns the median values of the elements along different dimensions of an array. A should be of type single or double.If A is a vector, median(A) returns the median value of A.If A is a matrix, median(A) treats the columns of A as vectors, returni

4、ng a row vector of median values. 第三章 概率與統計分析71. 統計分布的數字特征幾何平均值：幾何平均值：geomeanGeometric meanSyntaxm = geomean(x)geomean(X,dim)Descriptionm = geomean(x) calculates the geometric mean of a sample. For vectors, geomean(x) is the geometric mean of the elements in x. For matrices, geomean(X) is a row vect

5、or containing the geometric means of each column. For N-dimensional arrays, geomean operates along the first nonsingleton dimension of X.第三章 概率與統計分析81. 統計分布的數字特征調和平均值：調和平均值：harmmeanHarmonic meanSyntaxm = harmmean(X)harmmean(X,dim)Descriptionm = harmmean(X) calculates the harmonic mean of a sample. F

6、or vectors, harmmean(x) is the harmonic mean of the elements in x. For matrices, harmmean(X) is a row vector containing the harmonic means of each column. For N-dimensional arrays, harmmean operates along the first nonsingleton dimension of X.harmmean(X,dim) takes the harmonic mean along dimension d

7、im of X.第三章 概率與統計分析96.第三章 概率與統計分析101. 統計分布的數字特征標準差：標準差：stdStandard deviationSyntaxs = std(X)s = std(X,flag)s = std(X,flag,dim)s = std(X), where X is a vector, returns the standard deviation using (1) above. The result s is the square root of an unbiased estimator of the variance of the population fr

8、om which X is drawn, as long as X consists of independent, identically distributed samples.If X is a matrix, std(X) returns a row vector containing the standard deviation of the elements of each column of X. If X is a multidimensional array, std(X) is the standard deviation of the elements along the

9、 first nonsingleton dimension of X.第三章 概率與統計分析111. 統計分布的數字特征方差：方差：varVarianceSyntaxV = var(X)V = var(X,1)V = var(X,w)V = var(X,w,dim)DescriptionV = var(X) returns the variance of X for vectors. For matrices, var(X)is a row vector containing the variance of each column of X. For N-dimensional arrays,

10、 var operates along the first nonsingleton dimension of X. The result V is an unbiased estimator of the variance of the population from which X is drawn, as long as X consists of independent, identically distributed samples.第三章 概率與統計分析12例1. X 由下面的由下面的matlab命令流生成的矩陣：命令流生成的矩陣：X(:,1)=ones(10,1);X(1,1)=

11、100;X(10,1)=0.01;rand(state,1);randn(state,1)X(:,2)=rand(10,1);X(:,3)=randn(10,1);X(:,3)=2*abs(min(X(:,3)+X(:,3);求其平均值，中值，幾何平均值，調和平均求其平均值，中值，幾何平均值，調和平均值，標準差，方差。值，標準差，方差。X_mean=mean(X)X_mid=median(X)X_gmean=geomean(X)X_hmean=harmmean(X)X_std=std(X)X_var=var(X)第三章 概率與統計分析132.樣本分布的頻數直方圖描述histHistogram

12、plotSyntaxn = hist(Y)n = hist(Y,x)DescriptionA histogram shows the distribution of data values.n = hist(Y) bins the elements in vector Y into 10 equally spaced containers and returns the number of elements in each container as a row vector. If Y is an m-by-p matrix, hist treats the columns of Y as v

13、ectors and returns a 10-by-p matrix n. Each column of n contains the results for the corresponding column of Y. No elements of Y can be complex or of type integer.n = hist(Y,x) where x is a vector, returns the distribution of Y among length(x) bins with centers specified by x. For example, if x is a

14、 5-element vector, hist distributes the elements of Y into five bins centered on the x-axis at the elements in x, none of which can be complex. Note: use histc if it is more natural to specify bin edges instead of centers. 第三章 概率與統計分析14例2. x 由下面的由下面的matlab命令流生成的矩陣：命令流生成的矩陣：randn(state,1)rand(state,3

15、1)x=randn(100,1);y=rand(100,1);subplot(2,2,1),hist(x,7)subplot(2,2,2),histfit(x,20)subplot(2,2,3),hist(y,7)subplot(2,2,4),histfit(y,20)第三章 概率與統計分析15第三章 概率與統計分析163. 概率函數、分布函數、逆分布函數和隨機數的發生3.1 泊松分布(Poisson distribution)poisspdfPoisson probability density functionSyntaxY = poisspdf(X,lambda)DescriptionY

16、 = poisspdf(X,lambda) computes the Poisson pdf at each of the values in X using mean parameters in lambda. X and lambda can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other input. The pa

17、rameters in lambda must all be positive.第三章 概率與統計分析173.2 正態分布(Normal distribution)normpdfNormal probability density functionSyntaxY = normpdf(X,mu,sigma)DescriptionY = normpdf(X,mu,sigma) computes the pdf at each of the values in X using the normal distribution with mean mu and standard deviation si

18、gma. X, mu, and sigma can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs. The parameters in sigma must be positive.第三章 概率與統計分析183.3 2 分布（Chi-square distribution）chi2pdfChi-squar

19、e probability density functionSyntaxY = chi2pdf(X,V)DescriptionY = chi2pdf(X,V) computes the chi-square pdf at each of the values in X using the corresponding degrees of freedom in V. X and V can be vectors, matrices, or multidimensional arrays that have the same size, which is also the size of the output Y. A scalar input is expanded to a constant array with the same dimen