Robert_V._Hogg,_Joseph_W._McKean,_Allen_T._Craig
4.2. Confidence Intervals 245 4.2.4.In Example 4.2.4, for the baseball data, we found a confidence interval for the mean differe ...
246 Some Elementary Statistical Inferences getcis <- function(mat,cc=.90){ numb <- length(mat[,1]); ci <- c() for(j in ...
4.2. Confidence Intervals 247 4.2.17.It is known that a random variableX has a Poisson distribution with parameterμ. A sample of ...
248 Some Elementary Statistical Inferences 4.2.25.To illustrate Exercise 4.2.24, letX 1 ,X 2 ,...,X 9 andY 1 ,Y 2 ,...,Y 12 rep- ...
4.3.∗Confidence Intervals for Parameters of Discrete Distributions 249 random sample on a discrete random variableX with pmfp(x; ...
250 Some Elementary Statistical Inferences Example 4.3.2(Confidence Interval for a Bernoulli Proportion). LetX have a Bernoulli ...
4.3.∗Confidence Intervals for Parameters of Discrete Distributions 251 So the solution to the first equation isθ=0.434. In the s ...
252 Some Elementary Statistical Inferences poissonci(124,25,4,4.4,.95); $solution 4.287836 Since ppois(125, 25 ∗ 5 .5) = 0.1528 ...
4.4. Order Statistics 253 4.3.3.In Exercise 4.2.20, the large sample confidence interval was obtained for the probability that a ...
254 Some Elementary Statistical Inferences important role in statistical inference partly because some of their properties do no ...
4.4. Order Statistics 255 The pdf ofY 2 is then h(y 2 )=6f(y 2 ) ∫b y 2 ∫y 2 a f(y 1 )f(y 3 )dy 1 dy 3 = { 6 f(y 2 )F(y 2 )[1−F( ...
256 Some Elementary Statistical Inferences Thus P(^12 <Y 3 )= ∫∞ 1 / 2 g 3 (y 3 )dy 3 = ∫ 1 1 / 2 24(y 35 −y^73 )dy 3 = 243 2 ...
4.4. Order Statistics 257 Certain functions of the order statisticsY 1 ,Y 2 ,...,Ynare important statistics themselves. Thesampl ...
258 Some Elementary Statistical Inferences wheregk(yk)isthepdfofYkgiven in expression (4.4.2). If, in this integral, we make a c ...
4.4. Order Statistics 259 56 70 89 94 96 101 102 102 102 105 106 108 110 113 116 For these data, sincen+ 1 = 16, the realization ...
260 Some Elementary Statistical Inferences 110 100 x^90 80 Panel A 70 60 110 100 90 Sample quantiles 80 Panel B 70 60 1.5 –1.0 ...
4.4. Order Statistics 261 lower quantiles ofZmust be spread out as are the higher quantiles; i.e., symmetric distributions may b ...
262 Some Elementary Statistical Inferences that is,P[S≤cα/ 2 ]=α/2, whereSis distributedb(n, 1 /2). Then note also that P[S ≥n−c ...
4.4. Order Statistics 263 4.4.3.Consider the sample of data (data are in the fileex4.4.3data.rda): 13 5 202 15 99 4 67 83 36 11 ...
264 Some Elementary Statistical Inferences 4.4.10.LetY 1 <Y 2 <···<Ynbe the order statistics from a Weibull distributio ...
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