# Topic: Statistics

## Understanding Hypothesis Testing and p-value

Behavioral scientists, market researchers, astrophysicists, drug testers all seek to better understand the target group. Often it is next to impossible to assess the entire population. Inferential statistical testing is instead done on a sample that exhibits most if...## What is Hypothesis Testing

Many a times, we want to test the validity of a statement. For example, is the mean return from this mutual fund more to the mean return from the benchmark? While answering such a question, our interest is not to find the actual mean returns of the mutual fund, but to...## How to Read Student’s t Distribution Table (With PDF)

Student’s t distribution table has the following structure: The row represents the upper tail area, while the column represents the degrees of freedom. The body contains the t values. Note that for on-tail distribution the values are for a and for two-tailed...## Why Lognormal Distribution is Used to Describe Stock Prices

The concept of lognormal distribution is very closely related to the concept of normal distribution. Let’s say we have a random variable Y. This variable Y will have a lognormal distribution if the natural log of Y (ln Y) is normally distributed. So, we check if the...## How to Construct a Frequency Distribution

The statistical data that we collect can be presented in the form of a frequency distribution. A frequency distribution refers to summarizing a large data set into a small number of intervals. Let’s take an example to understand how to construct a frequency...## Best Linear Unbiased Estimator (B.L.U.E.)

The Need There are several issues when trying to find the Minimum Variance Unbiased (MVU) of a variable. The Probability Density Function (PDF) is not known It is difficult to model the PDF Even in cases where the PDF is known it is difficult to arrive at the estimate...## Linear Combinations of Random Variables

The joint distribution of a particular pair of linear combinations of random variables which are independent of each other is a bivariate normal distribution. It forms the basis for all calculations involving arbitrary means and variances relating to the more general...## Independent and Identically Distributed Variables

Definition I.I.D’s or independent and identically distributed variables are commonly used in probability theory and statistics and typically refer to the sequence of random variables. If the sequence of random variables has similar probability distributions but they...## Interpretation of Skewness, Kurtosis, CoSkewness, CoKurtosis

Kurtosis It indicates the extent to which the values of the variable fall above or below the mean and manifests itself as a fat tail. Within Kurtosis, a distribution could be platykurtic, leptokurtic, or mesokurtic, as shown below: If returns very high above or...