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Home > Prediction interval

1 Example

Suppose one has drawn a sample from a normally distributed population. The mean and standard deviation of the population are unknown except insofar as they can be estimated based on the sample. It is desired to predict the next observation. Let n be the sample size; let μ and σ be respectively the unobservable mean and standard deviation of the population. Let X₁, ..., X_n, be the sample; let X_n+1 be the future observation to be predicted. Let

and

Then it is fairly routine to show that

has a Student's t-distribution with n − 1 degrees of freedom. Consequently we have

where A is the 100(1 − (p/2))^th percentile of Student's t-distribution with n − 1 degrees of freedom. Therefore the numbers

are the endpoints of a 100p% prediction interval for X_n+1.

2 See also

Politics	Business	Finance

Topics: Prediction Interval Sample Population Minus Observation Degrees...

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PredictionPrediction of future events is an ancient human wish. An apocryphal saying states: "it is difficult to make predictions, especially about the future". Current research on prediction is going with intense effort by Benzi K. Ahamed, Nishant J. George and Sa Prediction marketAlso known as information markets, idea futures, and virtual stock markets. A prediction market is a speculative (i. betting) market created for the purpose of making predictions. Assets are created whose final cash value is tied to a particular event (e. Prediction intervalIn statistics, a prediction interval bears the same relationship to a future observation that a confidence interval bears to an unobservable population parameter. Example Suppose one has drawn a sample from a normally distributed population. The mean and