Sufficient statistic for normal distribution. For example, the sample...
Sufficient statistic for normal distribution. For example, the sample mean for a normal distribution is a sufficient statistic and is also an unbiased estimator. ” Let T = r(X1, · · · , Xn) be a sufficient statistic. Since the conditional distribution of X1, · · · , Xn given θ and T Apr 21, 2014 · Sufficient statistic for normal distribution with unknown mean and known variance Ask Question Asked 11 years, 10 months ago Modified 2 years ago While the definition of sufficiency provided on the previous page may make sense intuitively, it is not always all that easy to find the conditional distribution of \ (X_1, X_2, \ldots, X_n\) given \ (Y\). We must know in advance a candidate statistic \ (U\), and then we must be able to compute the conditional distribution of \ (\bs X\) given \ (U\). Statistician A knows the entire ran-dom sample X1, · · · , Xn, but statistician B only knows the value of T , call it t. A statistical hypothesis test typically involves a calculation of a test statistic. Again, assume there are n independent observations X i from a normal distribution N (μ, σ 2) with unknown mean and variance. Sufficient statistic means no other statistic would give additional information. For Gaussian mean and variance is enough to describe the distribution and so these are sufficient static for Gaussian. However, if μ is a known constant, then 1 n - 1 ∑ i = 1 n (X i - μ) 2 Aug 31, 2023 · A statistic is sufficient for a statistical model and a certain parameter if, roughly speaking, the knownledge of the sample offers no additional information than the statistic itself. bqrlstoaypniymozyvkdkhpofdfrjiwmamrzl