The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.
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One-tailed two-sample T-test OK?
I'm trying to conduct a one-sided hypothesis test between two random variables which are both asymptotically normally distributed with different variances. The variances are not known but have been ...
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1answer
38 views
Likelihood Cramér-Rao Bound.
How can I show the following necessary and sufficient condition?
An unbiased estimator $ \hat{\theta} $ of $ \theta $ achieves the Cramér-Rao Lower Bound if and only if
$$
\frac{\partial ...
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1answer
21 views
Predictive Power of X1 and X2
Two possible predictors, $X_1$ and $X_2$, are being considered when modelling a
response variable $Y$. The following two models are proposed;
$$\text{Model 1}: Y_i = 0 + 1X_{1i} + i$$
$$\text{Model ...
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1answer
35 views
How to find a mean, mode, and variance of a distribution problem?
I'm really not good in math, please bear with me. I searched and found some questions which are similar to this question. However, I cannot understand them.
I get doubt in this question for a day. ...
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1answer
36 views
Estimating the side of a square with random points
I have a square with side $\theta$ and origin in $(0,0)$. I simulate some random values inside the square's area. What is the maximum likelihhod estimator, confidence interval and a non-biased ...
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1answer
22 views
Inferring information about a population based on a sample
I think there is a simple statistical method for solving this type of problem. But my statistics knowledge is limited and rusty, so good explanations (or references to them) would be much ...
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332 views
Trying to understand the basics of bayesian inference
This paper gives a somewhat gentle introduction to Bayesian inference: http://www.miketipping.com/papers/met-mlbayes.pdf
I got to section 2.3 without much problems but got stuck in understanding that ...
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42 views
Probability distribution for a digit of a number
If someone choose a digit $\alpha$ and a digit $\beta$ independently. Each one can be in $0,1, ...,9$. So $\mu = \alpha \beta$ (e.g. if $\alpha = 5$ and $\beta = 3$ then $\mu =53$). And I observe a ...
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81 views
Sufficient Statistic for a Geometric R.V.
I have a problem that I know I am very close to the solution for, but I think I just need some more formatting to make it a really clean proof.
The problem goes like this:
Suppose X is a discrete ...
2
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0answers
44 views
Teaching Student's distribution
While it is fairly straightforward to show the basics of the normal distribution in a first year undergraduate course, how does a teacher provide good intuition when the Student distribution comes in? ...
2
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0answers
62 views
How do I must do it?
For a sample of size n from a random variable with density function $$f_{\theta}(x)=\frac{2x}{\theta^2}, x>0$$
find the confidence interval for $\theta$ of average length consistently lower level ...
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19 views
Inference the time a process would take depending on the number of threads
I have several datasets consisting on:
Number of threads n
Start process time t1
Stop process time ...
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61 views
Is there a statistical hypothesis test that uses the mode?
Is there a statistical hypothesis test that considers the mode rather than the mean or median?
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0answers
11 views
minimum distance estimation approach in inference
I am having a bit of problem with a very basic concept in the minimum distance estimation approach in statistical inference. I've read a paper which uses, for a parametric model family of discrete ...
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0answers
13 views
Run test statistics
I'm currently implementing the Wald-Wolfowitz runs test on a variable $\epsilon \in \{0;1\} $. According to the original paper, the number of runs, $V_n$ converges to the normal distribution with:
...
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0answers
27 views
Confidence interval for $k$
I have exams tomorrow and In preparing for it, I came across this question and I need help.
Suppose I have a random sample $ X_1, ..., X_n$ from a population with a density function $$f_{x}(x) = ...
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0answers
41 views
How do we estimate binomial confidence intervals when there are zero successes or failures?
Imagine I'm performing an experiment where I treat cells with some compound looking for toxicity. I test $N$ identical cells with the compound and all cells die immediately. As a function of $N$, ...
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176 views
Beta Distribution Sufficient Statistic
So I have this homework problem that I am struggling a little bit with coming to a solid answer on.
The problem goes like this:
Suppose X~Beta($\theta,\theta), (\theta>0)$, and let $\{X_1, X_2 , ...
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0answers
24 views
Test the hypothesis that $B_1=0$ at the $5 \%$ significance level
I am told to test the hypothesis and this is what I did:
$H_{0}:\beta_{1}=0$
$H_{a}:\beta_{1}\not=0$
So then I have $$t^{*}=\dfrac{\hat{\beta_{1}}-\beta_{1}}{\dfrac{s_{\beta_1}}{\sqrt n}}$$
...
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65 views
Need help deriving plug-in (functional of distribution) estimator
I need help with homework exercise, have no idea how to approach it.
Assume we have i.i.d. observations $x_1,\ldots,x_n$ of a continuous random variable $X$, taking values in $\mathbb R^+$. Define ...
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0answers
40 views
Classification: Why k-Nearest Neighbor method is more appropriate for a Mixture of Gaussians?
I'm reading a book named "The Elements of Statistical Learning" in which it states 2 scenarios when we are trying to predict the class label:
Scenario 1: The training data in each class were ...
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0answers
30 views
What is a good way to deal with finite trains from random variables?
EDIT:
Disregard this question if it is formulated too confusing.
This link provides you with the updated version of the same question
What is the most powerful test for process discrimination based ...
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73 views
What statistical hypothesis test to use for comparing results of two equations?
Given a function $f\left(x\right)$, I have two formulas to compute the coefficients of the same harmonic series approximation to $f\left(x\right)$. Call the results of each formula $^1c_k$ and $^2c_k$ ...
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25 views
Please show me that with which formula, I can calculate pooled variance for unequal population variance?
When equal population variances, I can calculate pooled variance (as like part-b)
But when unequal population variances, how to calculate pooled variance ( as like part-e)(also I underlined it ...
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12 views
sampling schemes for binomial distribution
Two acceptance sampling schemes, A and B, are proposed for deciding whether or not to accept a large batch of items from a production process in which 5% of the items produced are defective. Scheme A: ...
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46 views
Estimating the radius of a circle
I have a circle iwth radius $r$. I want to test the hypothesis that $r \leq 2$ vs. $r >2$ based on the posterior of $r$. $r$ follows the prior distribution: $f(r) = \frac{2}{r^{2}}$, $ r >0.5$. ...
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31 views
Infinite bucket of marbles
A question about statistics.
Suppose you are presented with an infinite bucket of marbles. You know there are 10 colors of marbles in the bucket, but that's all you know.
They could be either.
1. ...
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22 views
The sum of variable whith inverse Gauassian distribution
Let $ X_1,X_2,...,X_n$be a sample from inverse Gaussian pdf whith parameter $\mu$ and $\lambda$ .I want to show that
$\overline{X}$ has an inverse Gaussian distribution with parameter $\mu$ and ...
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12 views
About unit root tests
I have looking at unit root testing. Specifically 2 tests
ADF test
the ADF (augmented Dickey Fuller) is test which null hypothesis is "the time serie holds a unit root" (meaning that the time serie ...
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0answers
20 views
Equivalence of Bayes and Classical Sufficiency
According to [BLA], classical sufficiency implies Bayes sufficiency and, in the dominated case - all $P_\theta$ absolutely continuous w.r.t. a single measure - Bayes sufficiency implies classical ...
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33 views
Hypothesis Testing Bayesian Way
I'm having trouble with the following problem:
Suppose a machine is composed of 2 components (1 and 2, independent from each other). Each component has a exponential failure probability distribution ...
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29 views
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57 views
split plot design and sum of squares
How can we show that in a split plot design, the expected value of the sum-of-squares of the blocking factor has an expected value of to K*(sigma)^2_block + (sigma)^2_error?
I thought maybe using ...
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28 views
What is a topic I could easily collect data on that follows a poisson distribution?
So I have a project for my stat class and we have to form a hypothesis or question that I can do probabilistic modeling on. I really want to do a topic similar to a poisson distribution but I'm a ...
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76 views
Distribution of Sum of Discrete Uniform Random Variables
I just had a quick question that I hope someone can answer.
Does anyone know what the distribution of the sum of discrete uniform random variables is?
Is it a normal distribution?
Thanks!
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23 views
Variogram practical interprtation
I have 23 stations and I have calculated the variogram as following:
Variogram
The maximum distance between the stations is 2169 meter and the range is 1650 meter (exponential effective range).
I ...
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10 views
How would you approach weighting of open response lists in a statistical manner?
Imagine you asked a crowd of 1000 people what their top 10 movies were.
Crudely, you could give each participant's first selection a score of 10, 2nd = 9, 3rd = 8... 10th 1 value and build an ...
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35 views
Numerical calculation of fisher information
I am trying to obtain numerically the fisher information. Given a likelihood function
$$ f(X,\theta),$$
with $X \in [0,1]$.
The fisher information is given by
$$ ...
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16 views
Constructing a confidence interval for the mean from an approximation
The "classical" $(1-\alpha)$-confidence interval starts from the Student's t statistic $$t=\frac{\bar{x}-\mu}{s/\sqrt{n}}.$$
Then, one obtains the desired result, e.g. $\bar{x}\pm ...
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22 views
Wilcox rank-sum tests and permutation test
If I want to test group 1 has a larger location parameter than that of group 2. Assume the samples are independent and the size are both n. We can use (a) the Wilcox rank-sum tests or (b) the ...
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28 views
Bootstrapping with two-sample t-test
I'm estimating the population means of two samples using bootstrapping and am trying to determine if one is greater than the other. I bootstrapped 1000 times (i.e. calculated the mean of 1000 ...
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33 views
Survival Analysis
I have some survival times which are exponentially distributed for two groups G1 (treatment) and G2 (control). The data are censored with a censoring distribution given by h(c), so I only observe:
1) ...
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28 views
$\chi^2$ parameter of a data fit
So what is that parameter. When I make a non-linear fit, the program gives me a value $\chi^2/doF$. What is it?
I know some statistics and I know those $\chi^2$ distributions are used for ...
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0answers
34 views
first order auto regressive
Hello how to do the following:
Suppose that $X =(X_1,X_2,...,X_n)$ follows the following:
$X_t - \mu = \eta (X_{t-1} - \mu) + \epsilon_t,$ $t= 1,2,...$
where $\mu \in R$ and $\eta \in (-1,1)$ ...
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41 views
Struggling with proving an inconsistent estimator: Stat Theory
So I have this homework problem that goes:
Let X~exp(λ), with λ unknown, and let $X_1...X_n$ be a sample on X.
Show that T=$\sum X_i $ is not a consistent estimator for λ.
I know that the consistent ...
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52 views
Need a proof check for a Uniform Consistent Estimator: Statistical Theory
So I have a homework question that goes:
Let X~U$(0,\theta$). Show that Max($\{X_1, X_2 , \ldots , X_n \}$) is a consistent estimator for $\theta$.
From my class, we were shown that our CDF for Max ...
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83 views
Can Fumio Hayashi's econometrics book cover first-year graduate course?
Of course instructor or professor will recommend the book, but generally, does Fumio Hayashi book cover almost all of first-year graduate econometrics course?
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21 views
Likelihood function of two proportions
I'm starting studying maximum likelihood estimation, and I have came across to a problem that I don't know how to solve yet.
How can I write the likelihood function to test the hypothesis that some ...
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0answers
107 views
Find the efficiency of an unbiased estimator.
Let $X_1, X_2, X_3, \dots, X_n$ be a random sample from $N(\theta, \sigma)$, where $\sigma^2$ is known. If $Y=(X_1+X_2)/2$ is an unbiased estimator of $\theta$, what is the efficiency of $Y$?
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49 views
confidence interval
A telecommunication sales representative is responsible to sell various products such as wireless
equipment, satellite dishes and internet access. One particular sales representative working for
the ...
