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Student T-Density Function-ECO6416

Student T-Density Function-ECO6416 - As the...

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Student T-Density Function The t distributions were discovered in 1908 by William Gosset , who was a chemist and a statistician employed by the Guinness brewing company. He considered himself a student still learning statistics, so that is how he signed his papers as pseudonym “Student". Or, perhaps he used a pseudonym due to “trade secret" restrictions by Guinness. Note that there are different t-distributions; it is a class of distributions. When we speak of a specific t distribution, we have to specify the degrees of freedom. The t density curves are symmetric and bell-shaped like the normal distribution and have their peak at 0. However, the spread is more than that of the standard normal distribution. The larger the degrees of freedom, the closer the t-density is to the normal density. The shape of a t-distribution depends on a parameter called “degree-of-freedom".
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Unformatted text preview: As the degree-of-freedom gets larger, the t-distribution gets closer and closer to the standard normal distribution. For practical purposes, the t-distribution is treated as the standard normal distribution when degree-of-freedom is greater than 30. Suppose we have two independent random variable s, one is Z, distributed as the standard normal distribution, while the other has a Chi-square distribution with (n-1) d.f.; then the random variable : (n-1)Z / χ 2 has a t-distribution with (n-1) d.f. For large sample size (say, n over 30), the new random variable has an expected value equal to zero, and its variance is (n-1)/(n-3) which is close to one. Notice that the t- statistic is related to F-statistic as follow: F = t 2 , where F has (d.f. 1 = 1, and d.f. 2 = d.f. of the t-table) You might like to use Student t-Density to obtain its P-values....
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