What does distribution mean in statistics

To obtain the one-tailed probability, divide the two-tailed probability by 2. So the probability that the sample mean is greater than 22 is between 0. All Rights Reserved. Date last modified: January 6, If X is approximately normally distributed, then has a t distribution with n-1 degrees of freedom df Using the t-table Note: If n is large, then t is approximately normally distributed.

From the tables we see that the two-tailed probability is between 0. The number 2. Because the T distribution has fatter tails than a normal distribution, it can be used as a model for financial returns that exhibit excess kurtosis, which will allow for a more realistic calculation of Value at Risk VaR in such cases. Normal distributions are used when the population distribution is assumed to be normal. The T distribution is similar to the normal distribution, just with fatter tails.

Both assume a normally distributed population. T distributions have higher kurtosis than normal distributions. The probability of getting values very far from the mean is larger with a T distribution than a normal distribution.

The T distribution can skew exactness relative to the normal distribution. The T-distribution should only be used when population standard deviation is not known.

If the population standard deviation is known and the sample size is large enough, the normal distribution should be used for better results. Tools for Fundamental Analysis.

Risk Management. Financial Ratios. Portfolio Management. Your Privacy Rights. To change or withdraw your consent choices for Investopedia.

At any time, you can update your settings through the "EU Privacy" link at the bottom of any page. These choices will be signaled globally to our partners and will not affect browsing data. We and our partners process data to: Actively scan device characteristics for identification. I Accept Show Purposes. Develop and improve products. List of Partners vendors. A probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range.

This range will be bounded between the minimum and maximum possible values, but precisely where the possible value is likely to be plotted on the probability distribution depends on a number of factors. These factors include the distribution's mean average , standard deviation , skewness , and kurtosis. Perhaps the most common probability distribution is the normal distribution, or " bell curve ," although several distributions exist that are commonly used.

Typically, the data generating process of some phenomenon will dictate its probability distribution. This process is called the probability density function. Academics, financial analysts and fund managers alike may determine a particular stock's probability distribution to evaluate the possible expected returns that the stock may yield in the future. The stock's history of returns, which can be measured from any time interval, will likely be composed of only a fraction of the stock's returns, which will subject the analysis to sampling error.

By increasing the sample size, this error can be dramatically reduced. There are many different classifications of probability distributions. Some of them include the normal distribution, chi square distribution, binomial distribution , and Poisson distribution. The different probability distributions serve different purposes and represent different data generation processes. The binomial distribution, for example, evaluates the probability of an event occurring several times over a given number of trials and given the event's probability in each trial.

Another typical example would be to use a fair coin and figuring the probability of that coin coming up heads in 10 straight flips. A binomial distribution is discrete , as opposed to continuous, since only 1 or 0 is a valid response.

The most commonly used distribution is the normal distribution, which is used frequently in finance, investing, science, and engineering. The normal distribution is fully characterized by its mean and standard deviation, meaning the distribution is not skewed and does exhibit kurtosis. This makes the distribution symmetric and it is depicted as a bell-shaped curve when plotted. A normal distribution is defined by a mean average of zero and a standard deviation of 1.

Unlike the binomial distribution, the normal distribution is continuous, meaning that all possible values are represented as opposed to just 0 and 1 with nothing in between. Stock returns are often assumed to be normally distributed but in reality, they exhibit kurtosis with large negative and positive returns seeming to occur more than would be predicted by a normal distribution. In fact, because stock prices are bounded by zero but offer a potential unlimited upside, the distribution of stock returns has been described as log-normal.

This shows up on a plot of stock returns with the tails of the distribution having greater thickness. Probability distributions are often used in risk management as well to evaluate the probability and amount of losses that an investment portfolio would incur based on a distribution of historical returns.

One popular risk management metric used in investing is value-at-risk VaR.