Tagged Questions

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What is sampling with unequal probabilities without replacement

sampling without replacement: i know if my sample size is $n$, and if $i^{th}$ unit is drawn then we will not replace the unit in the population , so that in my next draw i can get any unit except ...
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“Approximation” of a maximum likelihood confidence set

I have some trouble constructing the "approximate" set, how can it be defined or calculated? Suppose that three characteristics in a large population can be observed according to the following ...
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Alternatives to absolute error?

Let me explain my scenario in which I need to calculate absolute error. Lets say the X is the actual value. And X' is the value of X with some error 'e'. So X' = X + e'. Lets say i = 1 to 10000. I ...
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UMVUE using complete and sufficient statistic

Let $X_1,X_2,...,X_n$ be a random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. I showed that $(\bar X,S^2)$ is jointly sufficient for estimating ($\mu$,$\sigma^2$) where ...
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Question about English sentences in statistics?

Can somebody help me interpreting the red circled sentences in planer English? I understand "We view $y_i$ as a realization of a random variable $Y_i$ that can take the values of one and zero" but ...
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Consequences of violation of independence assumption in ANOVA test

Can you please explain me what is the consequences of violation of independence assumption in ANOVA test? I couldn't visualize it. Does Cochran Theorem relates to ...
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P-P plot and Q-Q plot

How to draw P-P plot and Q-Q plot manually ? I have looked at different site and they explained in various way, such as one said for p-p plot in X-axis there is residual in ascending order and in ...
Question: Let $X_1$, $X_2$, and Z denote independent, real-valued random variables. Assume that $Pr(Z=0) = 1 - Pr(Z=1)$ = $\alpha$ for some $0 < \alpha < 1$. Define $Y = \left\{ ... 1answer 13 views Confidence interval for difference in means I need to obtain a 95% confidence interval for the indifference in the mean score overall I have the following data which states subject (A-L) and then Test and Retest A B C D E F G H I J K ... 1answer 16 views Chi square test, double counting? We're testing whether three species are affected differently by some poison, getting this table (type/dead/alive/tot): A, 10, 20, 30 B, 16, 14, 30 C, 22, 8, 30 Under H0, we're expeting 16 to live ... 1answer 31 views Cross-Validation Does anyone understand the paragraph below? The paragraph comes from Cross-valiation explanation at wikipedia. "It can be shown under mild assumptions that the expected value of the MSE for the ... 1answer 17 views Is the statement:$p\left(\left.y\right|h^{-1}\left(\varphi\right)\right)=p\left(\left.y\right|\varphi\right)$correct? Say I have a likelihood function$p\left(\left.y\right|\theta\right)$and I make the reparameterization$\varphi=h\left(\theta\right)$using the bijective function$h$with inverse$h^{-1}$. Then it ... 1answer 31 views Doubts on Bayes hypothesis test I meet one problem on hypothesis testing in statistic theory. "Assume given the probability spaces$(X,S,\mu_i)$,$i=1,2$.$H_i$,$i=1,2$, is the hypothesis that$T$is from the statistical ... 1answer 53 views Better estimators with absolute function pdf I have some pdf$f(x|\theta) = (\theta/2) ^ {|x|} \cdot (1 - \theta) ^ {(1 - |x|)}$where$x = -1, 0, 1$, and$0 \le \theta \le 1$. I found the MLE of theta by denoting$n_{-1}$the number of ... 1answer 22 views Decompose a sum of Gaussian curves I have a data set with 2 different curves in a .csv file. Both curves are a sum of Gaussian curves and I'd like to be able to decompose these curves into their substituent addends: ... 0answers 15 views Calculating person-time Suppose that an investigator wants to measure the incidence rate of high blood pressure in the$1997-98$freshman class of a university. Assume that there were$1000$entering freshmen and that this ... 1answer 17 views Uncertainty on an estimator Well first I want to say that I have a very weak background in stats/probability but I still hope that the question I want to share with you makes sense. I have a set of binary (coming from a set of ... 1answer 11 views Statistics Sample requirements In statistics , a sample should be random, have a sample size less than one-tenth of the population and be normally distributed for it to be viable for simple statistical analysis. I understand fully ... 1answer 63 views Normalization for Chi square test The formula for the Chi-Square test statistic is the following:$\chi^2 = \sum_{i=1}^{n} \frac{(O_i - E_i)^2}{E_i}$where O - is observed data, and E - is expected. I'm curious why it depends on ... 4answers 49 views The Objectivity of Statistical Testing I have a very generic question about applied statistics. Suppose, to make things simple, we have a biased coin with probability$p$of landing heads. We want to determine if our coin is truly fair - ... 0answers 29 views Proving a statistic is sufficient and NOT complete Let X be a single observation from the distribution ,$P(X=x)= \begin{cases} \theta, & \text{if $x$ =-1} \\ (1-\theta)^2\theta^x, & \text{if $x =0,1,2,3,...; 0<\theta<1$} \\ ...
Let X from a Normal distribution $(\theta,1)$. a) Find a sufficient statistic for $\theta$. b)Is $S_n^2$ sufficient for $\theta$ My answer for part a) The joint p.d.f= $1 \over (2\pi)^{n/2}$\$e^{{-1 ...