Shree GaneshA Statistics

 

 Examples on calculating correlation coefficient.  To calculating correlation coefficient: There are three methods of calculating r. i.    Actual Mean method. ii. Step Deviation Method. iii. Assumed Mean Method. We see the one by one methods The another method of calculating the correlation is Spearman's Rank Correlation. this is an another method of calculating the correlation coefficient in simple way than the  Karl Pearson’s  developed by Spearman's. in this method the correlation is calculated based on the rank of the observations.  the rank correlation coefficient between x and y is 0.2857 Regression Notes

 Statistical Inference Mcq's tomorrow i will add new questions Certainly, I'll be here to answer your question tomorrow. Feel free to ask whenever you're ready, and I'll provide you with the answer.

 Correlation In previous blog we discussed about the measure central tendency and Dispersion to use to study the variable. the correlation is a statistical concept that allows us to measure and understand the relationship between two or more variables. it provided a valuable information about that variables. e.g. price and demand of commodity, income and expenditure of family, height and weight of group of persons. their we use the relation   between this two variables. in above examples we see the one variable increases other variable is also changes in same or opposite direction.  definition: Correlation is statistical tool which study the relationship between two or more variables. for analysis of correlation various method and techniques are used.  example: i. Demand and supply of product                                                                                                                                                     ii. price and demand                            

 Statistical Inference I: Method Of Moment:   One of the oldest method of finding estimator is Method of Moment, it was discovered by Karl Pearson in 1884.  Method of Moment Estimator Let X1, X2, ........Xn be a random sample from a population with probability density function (pdf) f(x, θ) or probability mass function (pmf) p(x) with parameters θ1, θ2,……..θk. If μ r ' (r-th raw moment about the origin) then μ r ' = ∫ -∞ ∞ x r f(x,θ) dx for r=1,2,3,….k .........Equation i In general, μ 1 ' , μ 2 ' ,…..μ k ' will be functions of parameters θ 1 , θ 2 ,……..θ k . Let X 1 , X 2 ,……X n be the random sample of size n from the population. The method of moments consists of solving "k" equations (in Equation i) for θ 1 , θ 2 ,……..θ k to obtain estimators for the parameters by equating μ 1 ' , μ 2 ' ,…..μ k ' with the corresponding sample moments m 1 ' , m 2 ' ,…..m k ' . Where m r ' = sample m

Changing Color Blog Name Statistical Inference I: (Cramer-Rao Inequality, Method Of Moment, Maximum Likelihood Estimator) I. Introduction We see in unbiased estimator from two distinct unbiased estimators give infinitely many unbiased estimators of θ, among these estimators we find the best estimator for parameter θ by comparing their variance or mean square errors. But in some examples, we see that the number of estimators is possible as. For Normal distribution: If X1, X2, ........Xn. random sample from a normal distribution with mean 𝛍 and variance 𝛔², then T1 = x̄, T2 = Sample median, both are unbiased estimators for parameter 𝛍. Now we find a sufficient estimator; therefore, T1 is a sufficient estimator for 𝛍, hence it is the best estimator for parameter 𝛍. Thus, for finding the best estimator, we check if the estimator is sufficient or not. Now we are interested in finding the variance of th