# t-distribution

Pick the most correct answer. t-distribution’s kurtosis is a) greater than 3 b) less than 3 c) depends on the sample for which t distribution is being approximated d) is not equal to 3 Once you answer this, please explain.

C: you have to have a degree of freedom in a t-distribution.

t-distribution has thinner tails than normal it is platykurtic with kurtosis<3 (i.e. its lies below the normal) the more degrees of freedom a t-dist has, the closer it gets to normal dist’n (kurtosis grows)

supersharpshooter Wrote: ------------------------------------------------------- > t-distribution has thinner tails than normal > I thought t-distrubtion has fatter tails than normal, more area under tails.

if a is correct, d is correct if b is correct, d is correct however we can’t pick two answers so the answer must be c i agree degree of freedom matters

oops yeah i have it the other way around t-distribution has fatter tails than normal it has kurtosis>3 the more degrees of freedom a t-dist has, the closer it gets to normal dist’n (kurtosis becomes lower) i pick a) greater than 3 can anyone comment?

heha168 Wrote: ------------------------------------------------------- > if a is correct, d is correct > if b is correct, d is correct > however we can’t pick two answers > so the answer must be c > > i agree degree of freedom matters The question says, most correct answer. again I made this question and choices, so no one really knows what answer is, but I hope we get the concept clear.

supersharpshooter Wrote: ------------------------------------------------------- > oops yeah i have it the other way around > > t-distribution has fatter tails than normal > > it is lepokurtic with kurtosis>3 > > the more degrees of freedom a t-dist has, the > closer it gets to normal dist’n (kurtosis becomes > lower) > > i pick a) greater than 3 > > can anyone comment? ok, t distribution definitely has fatter tails than normal,but it is also less peaked than normal, so???

less than 3- t used when sample size is ,30, so short height but fat tail.

i am pretty sure a t distribution is lepokurtic

pepp Wrote: ------------------------------------------------------- > supersharpshooter Wrote: > -------------------------------------------------- > ----- > > oops yeah i have it the other way around > > > > t-distribution has fatter tails than normal > > > > it is lepokurtic with kurtosis>3 > > > > the more degrees of freedom a t-dist has, the > > closer it gets to normal dist’n (kurtosis > becomes > > lower) > > > > i pick a) greater than 3 > > > > can anyone comment? > > ok, t distribution definitely has fatter tails > than normal,but it is also less peaked than > normal, so??? i thought fat tails and peaks happen concurrently. not the case?

with df = 1, it’s platykurtic, and as df increase, it becomes mesokurtic.

T- distribution mean less confidence around the mean —> more observations lie far from the mean ----> fat tail —> platykurtic —> kurtosis < 3

Fat Tail, Platykurtic, and so the kurtosis is less than 3. The kurtosis of a normal dist. is 3. As n gets larger and larger, a t-dist will start to become more like a normal dist; i.e. more peaked and thinner tails… It “grows”, so to speak…