PROBABILITY DISTRIBUTION Dr.Fatima Alkhalidi

PROBABILITY DISTRIBUTIONS We usually compare our observations in the studies with a theoretical probability distribution which is described by a mathematical models. Depending on whether the random variable is discrete or continuous, the probability distribution can be either discrete or continuous.

Discrete probability distribution 1. Binomial distribution  

Discrete probability distribution 2. Poisson distribution Used to determine the probability of the rare events, when the average number of successes is known.

Continuous probability distribution we can only derive the probability of the random variable if it is continuous variable. Continuous pr. Distributions include (Normal test (z test), t test, F test and Chi squared test)

The Normal Distribution “Gaussian Distribution” It is the most important distribution in statistics The parameters in this distribution are the: Population mean (µ) as a measure of central tendency Population standard deviation (σ) as a measure of dispersion

Mode Median

The Normal Distribution “Gaussian Distribution” It is used for continuous variables The curve is symmetric around the mean The total area under the curve equal one The mean, median, and the mode are equal

The Normal Distribution “Gaussian Distribution” 50% of the area under the curve is on the right side of the curve and the other 50% is on its left. Not kurtotic and not skewed.

Skewness Refers to the degree of asymmetry of the distribution of the variable. It is skewed to the right (+ve) , it has long tail to the right with few high values ( the mean is larger than the median). It is skewed to the left(-ve) , it has long tail to the left with few low values ( the mean is smaller than the median). So the median is more stable than the mean

Kurtosis Refers to the ‘peakedness’ of the distribution. The flat curve is called platykurtotic. The peaked curve is called leptokurtotic.