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Statistics48

Maximum likelihood estimator/ exponential,poisson,binomial,bernoulli,Normal,uniform/ Invariance property/ consistency/ central limit theorem/slutsky's theorem There are two typical ways which are Maximum likelihood estimation and Methods of moments to be used in estimation for parameters. For this post, I will introduce Maximum likelihood estimator as method for estimation. Because log function is the monotonic increase function, a parameter which makes likelihood function of Θ be maximized also makes log(likelihood function of Θ) be maximized. And wh.. 2020. 8. 20.
Chi-Square distribution Chi-Square distribution Chi-Square distribution is a distribution with parameter n which is called 'degree of freedom.'The distribution is closely related to Normal distribution and Gamma distribution. Specifically, it is a critical distribution when it comes to samples and variance of normal distribution. Also, it is a special case of Gamma distribution with specific parameters. The first prope.. 2020. 8. 6.
Exponential family Exponential Family Exponential family is a specific probability distribution of a certain form. In statistics, there are some properties that distributions of exponential family have in common. and lots of familiar distributions including exponential distribution, Bernoulli, Beta, Gamma, Poisson, Negative Binomial, Geometric, chi-squared, normal distribution are the form of exponential family. I.. 2020. 8. 6.
Relationship between Beta distribution and standard uniform distribution Relation between Beta(a,b) and U(0,1) Beta distribution and standard uniform distribution which is a special case of uniform distribution with 0,1 has some relationships. Firstly, Beta(1,1) and U(0,1) look exactly the same distributions and secondly, order statistics of U(0,1) looks same with beta distribution with specific parameters. Firstly, let's take a look at basic information of two distr.. 2020. 8. 5.
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