Create Google File Dowanload Links in A Different Way
Posted: August 25, 2022 #HTML+CSSGoogle Drive is a powerful app to store files of pdf, word, excel and other formats. If you create a copy link from google drive and embed the link into your webpage directly, the default setting is that when user click on the download link, browser will open the file in google doc viewer in a ne...
Video Embeding and Styling on Webpages
Posted: August 19, 2022 #HTML+CSSTable of Contents: Introduction Video From Cloud How to find google photo link How to style the video Google drive as a backup Okay, not a good solution Video from Youtube Youtube example: Introduction This post is based on conten...
Finding Student t Distribution
Posted: May 9, 2022 #StatsIn reality we may never know the variance of the population, and we have only a limited sample size due to economical reason as well as other restraints. It turns out the pdf of t ratio is not exactly the same as normal distribution. Oxford graduate William Sealy Gossett published a paper in 190...
The Generalized Likelihood Ratio
Posted: May 3, 2022 #StatsWe’ve already known that in hypothesis testing, we have a null hypothesis, where $ H_0: \theta = \theta_0$ versus alternative hypothesis $H_A: \theta \neq \theta_0$. We also have a presumed pdf function for the variables. Based on these information, we can construct a critical point/region when w...
Bayesian Estimation
Posted: April 21, 2022 #StatsEven if we can pick the correct pdf model for the whole population of data, we may never know the true parameters for such models. We construct different kinds of functions to evaluate the parameters, which we call point estimators. We feed sample data to the function and get the result, i.e., es...
Sufficient Estimators
Posted: April 11, 2022 #StatsAfter the expected value and variance of an estimator, we now discuss a third feature: sufficiency. Whether or not an estimator is sufficient refers to the amount of “information” it contains about the unknown parameter $\theta$. We start by defining what sufficient means for an estimator for tru...
The Cramer-Rao Theorem
Posted: April 3, 2022 #StatsThe Cramér-Rao Inequality theorem provides a lower bound for the variance of an unbiased estimator of a density function parameter. Many statistics textbooks provide the theorem without giving any proof, which sometimes frustrates students like me. I therefore did some research online and referre...
The Sample Median Theorem
Posted: April 2, 2022 #StatsThe Central Limit Theorem is one of the gems in probability realm. Another important and related theorem is about the sample median. It says that the density of the median of a sample, if the sample size goes large enough, will also follow a normal distribution. This note will try to establish a ...
Interval Estimation
Posted: March 28, 2022 #StatsWe can get the estimate for parameters based on a survey of $n$ results, either by the method of maximum likelihood or moments. For example, we have $\lambda = X$ as the estimator for a Poisson parameter, $\lambda$. Now we need to consider another question: how close is this estimated $\lambda_e...
How to find pdf for sum, quotient and difference of variables
Posted: March 19, 2022 #StatsGiven pdf of two independent varialbes, how can we find the pdf of their sum, quotient or differnece? Although this is a basic technique in statictics, but it finds its application in a very broad scope. Read more