概率与统计分析.pptx

MATLAB 程序设计 1 MATLAB 程序设计 道路与桥梁工程系 副主任 Department of Civil Engineering Hefei University of Technology ; 主讲人：王佐才 “黄山青年学者教授” 第三章 概率与统计分析 2 本章内容： 统计分布的数字特征 样本分布的频数直方图描述 概率函数、分布函数、逆分布函数和随机数的发生 第三章 概率与统计分析 3 1. 统计分布的数字特征 平均值： mean Average or mean value of array Syntax M = mean(A) M = mean(A,dim) Description M = mean(A) returns the mean 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 概率与统计分析 4 1. 统计分布的数字特征 中值： median Median value of array Syntax M = median(A) M = median(A,dim) Description M = 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, returning a row vector of median values. 第三章 概率与统计分析 5 1. 统计分布的数字特征 几何平均值： geomean Geometric mean Syntax m = geomean(x) geomean(X,dim) Description m = 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 vector containing the geometric means of each column. For N-dimensional arrays, geomean operates along the first nonsingleton dimension of X. 第三章 概率与统计分析 6 1. 统计分布的数字特征 调和平均值： harmmean Harmonic mean Syntax m = harmmean(X) harmmean(X,dim) Description m = harmmean(X) calculates the harmonic mean of a sample. For 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 dim of X. 第三章 概率与统计分析 7 1. 统计分布的数字特征 标准差： std Standard deviation Syntax s = 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 from 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 first nonsingleton dimension of X. 第三章 概率与统计分析 8 1. 统计分布的数字特征 方差： var Variance Syntax V = var(X) V = var(X,1) V = var(X,w) V = var(X,w,dim) Description V = 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, 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 概率与统计分析 9 例1. X 由下面的matlab命令流生成的矩阵： X(:,1)=ones(10,1); X(1,1)=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，几何平均值，调和平均 值，标准差，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 概率与统计分析 10 2.样本分布的频数直方图描述 hist Histogram plot Syntax n = hist(Y) n = hist(Y,x) Description A 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 vectors 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 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 概率与统计分析 11 例2. x 由下面的matlab命令流生成的矩阵： randn(state,1) rand(state,31) 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 概率与统计分析 12 第三章 概率与统计分析 13 3. 概率函数、分布函数、逆分布函数和随机数的发生 3.1 泊松分布(Poisson distribution) poisspdf Poisson probability density function Syntax Y = poisspdf(X,lambda) Description Y = 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 parameters in lambda must all be positive. 第三章 概率与统计分析 14 3.2 正态分布(Normal distribution) normpdf Normal probability density function Syntax Y = normpdf(X,mu,sigma) Description Y = normpdf(X,mu,sigma) computes the pdf at each of the values in X using the normal distribution with mean mu and standard deviation sigma. 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 概率与统计分析 15 3.3 2 分布（Chi-square distribution） chi2pdf Chi-square probability density function Syntax Y = chi2pdf(X,V) Description Y = 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