Definition The most basic form of continuous probability distribution function is called the uniform distribution. It is a rectangular distribution with constant probability and implies the fact that each range of values that has the same length on the distributions support has equal probability of occurrence. This belongs to the category of maximum entropy probability […]
Distributions - FRM
Properties of Bernoulli Distribution
Definition The Bernoulli distribution is a discrete probability distribution which consists of Bernoulli trials. Each Bernoulli trial has the following characteristics: There are only two outcomes a 1 or 0, i.e., success or failure each time. If the probability of success is p then the probability of failure is 1-p and this remains the same […]
Properties of Normal Distribution
Definition It is one of the most important continuous probability distributions which finds wide applications in real life by describing variables that display randomness. The distribution is characterized by bell curve which is more weight in the center and tapers off on either side which means it has tails on either side. It takes only […]
Paramteric vs Non-Parametric Distributions
Definitions Parametric Distribution: A parametric distribution is used in statistics when an assumption is made of the way the underlying data is distributed. An example would be when a variable is assumed to be normally distributed. All subsequent analysis will then rely on this assumption. The parameters associated with this assumption like mean and standard […]
Properties of Log-Normal Distribution
Definition If the logarithm to the power of the variable x is normally distributed then the variable itself is said to be lognormally distributed. In other words if ln(x) is normally distributed then the variable x is supposed to have a log-normal distribution. The probability density function for this variable is as follows: In this […]
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 are independent of each other then the variables are called independent and identically distributed variables. This is a […]
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 bivariate normal distribution. The property of rotational symmetry implies that the joint distribution of […]