Tagged Questions

Mathematical theory of statistics, concerned with formal definitions and general results.

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0
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0answers
23 views

Unsupervised learning algorithems to detect anomaly in waves

I have a sample of graphs (more then 10000...). that look like in the image below: I am searching an Unsupervised learning algorithems thet can help me to detect Anomaly observations. Here what i ...
0
votes
1answer
20 views

Fisher information always 0? What's wrong with this argument?

We exchange derivative and integral while proving that the expected value of the score is 0. Here is the proof which does so: \begin{align*} \int \left( \frac{\partial}{\partial \theta} \log ...
0
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0answers
7 views

Minitab need help [on hold]

I need to create a comparison histogram using minitab. Anyone can teach me to the steps in doing that? EG
0
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0answers
23 views

Is the mvrnorm function in Julia unstable?

I am trying to sample multivariate samples using mvrnorm in julia. Arguments are set as: mean5 = zeros(5) cov5 = the cor(z1, z2, z3, z4, z5), where z_i is calculated as x1,x2 ~Normal(0, 1) iiid ...
0
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0answers
17 views

how many way can we arrange …? [on hold]

In how many ways can we arrange two letters, two numbers, and one character (such as dot symbol ".")? where: * The two letters can not be repeated. * The two numbers can not be repeated. * The number ...
6
votes
1answer
75 views

What are some good references on how probability theory got mathematically rigorous?

I am working on a term paper for an analysis course and I thought it would be interesting to talk about the connection between analysis and probability theory. Honestly, it would also benefit me a lot ...
8
votes
1answer
98 views

Why is the definition of a consistent estimator the way it is? What about alternative definitions of consistency?

Quote from wikipedia: In statistics, a consistent estimator or asymptotically consistent estimator is an estimator—a rule for computing estimates of a parameter $θ^*$—having the property that ...
0
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0answers
7 views

Maximum entropy distribution >0 with vanishing probability at zero?

I know that the maximum entropy distribution if x > 0 and the mean is known is the exponential distribution. However, a large percentage of the probability for this distribution is close to zero ...
1
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1answer
51 views

Deriving the maximum likelihood for the parameters in linear regression

Notation: $\textbf{w}$ is an M-dimensional vector of parameters (including the bias parameter), $\textbf{x}_n$ is an M-dimensional vector of the features of each training example, $\textbf{t}$ is an ...
1
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0answers
11 views

Kullback Leibler divergence “efficient” upper bound

For a distribution of N values, how can I efficiently upper-bound the largest divergence between all non-negative distributions over the same random field? For example, for all distributions of a ...
1
vote
1answer
35 views

What statistical analysis should I use for my study?

In my psych class we were testing to see if groups of men or groups of women would be more helpful in an emergency situation (we are testing for the bystander effect), and we are testing to see if ...
0
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0answers
7 views

Weighted Standard Deviation [duplicate]

I got a problem calculating a weighted standard deviation for a municipality and its precipitation on various landcover types (LC). I got the mean values of precipitation for several days for each ...
1
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0answers
20 views

Calculating the probability of both teams to score in a soccer match?

New to the forum, and while not quite an idiot, I have no where near the knowledge and nous of all in here. Consider the following scenario: Soccer match Home team - Team A Away team - Team B ...
0
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0answers
12 views

What “randomness induces dependencies” and “estimates … exhibit shrinkage” mean?

I am reading a paper named "Hierarchical Dirichlet Processes", whose first paragraph reads A recurring theme in statistics is the need to separate observations into groups, and yet allow the groups ...
0
votes
1answer
71 views

which distribution should be used in this question?

A basketball player succeeds in making a basket three tries out of four. How many times must he try for a basket in order to have greater than 0.99 probability of making at least one basket? In this ...
1
vote
1answer
58 views

In a two-way ANOVA, how can the F-statistic for one factor have a central distribution if the null is false for the other factor?

Consider the two factor additive ANOVA model $$\begin{align} X_{ij} &=\mu_{ij}+e_{ij} \\ \mu_{ij}&=\mu+\alpha_i+\beta_j \end{align}$$ where as usual $\sum_{i=1}^a \alpha_i=0$ and ...
-1
votes
1answer
51 views

Indepent variables and these functions [closed]

Random variables $x_1, x_2,...,x_n$ are independent. Then I want to show whether these functions $$y_1=f_1(x) \\ y_2=f_2(x) \\ ... \\ y_n=f_n(x)$$ are independent or not . How to prove this?
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0answers
5 views

Using Quality metrics of BIRCH Clusters

What is significance of quality metrics of BIRCH Clusters Distance3 and Distance4. Appreciate if there are pointers are how to use Average Intra Cluster Distance (D3) and Average Inter Cluster ...
0
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0answers
19 views

Spline surface data fitting with constraints

I'm trying to smooth surface-fit experimental results on 2D domain (x,y), while maintaining common sensce physics-based constraints (monotonous, convex, etc.). current procedure is hand-draw lines ...
1
vote
1answer
32 views

Derivative of power spectral density

The power spectral density (PSD) of an AR(p) model excited by a white Gaussian noise input $u(t)$ of variance $\sigma_u^2$ is $P_{xx}(f:\theta) = \frac{\sigma_u^2}{|A(f)|^2}$ where $\theta = ...
0
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0answers
15 views

Staffing Requirement Model Is my Erlang C approach correct?

If I am running an Erlang C model which is commonly used to analyze call center performance . However, there are different tasks involved not just answering calls. I am calculating the traffic ...
3
votes
2answers
82 views

A random variable that induces a $\sigma$-algebra the same as the one in the sample space

Consider a probability space $(\Omega, \mathcal{F}, P)$ where $\Omega$ is the sample space, $\mathcal{F}$ is the $\sigma$-algebra of $\Omega$, and $P$ is the probability measure. Let ...
0
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0answers
34 views

Getting Sample size

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between \$35,000 and \$50,000 (Hint: Refer to the last slide of your Chapter 8 ...
5
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1answer
157 views

Estimating parameters for a binomial

First of all I'd like to precise that I'm not an expert of the subject. Suppose to have two random variables $X$ and $Y$ that are binomial, respectively $X\sim B(n_1,p)$ and $Y\sim B(n_2,p),$ note ...
3
votes
1answer
44 views

Need an Introduction to Generalized Non Linear Multiple Regression

I have been searching the internet for a generalized method for doing regression analysis on non linear data. My model can be represented as $$Y = \beta_0f(X_0) + \beta_1g(X_1) + ... + \beta_nz(X_n) ...
2
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0answers
31 views

intuition for moments about the mean of a distribution?

can someone provide an intuition on why the higher moments of a probability distribution p(x) like the third and fourth moments correspond to skewness and kurtosis, ...
0
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0answers
12 views

Parametric or non-paramateric? [duplicate]

Actual 1100 1300 1400 1500 1600 1100 1200 1600 2100 1300 1600 1300 1600 2200 2300 1700 1800 800 1400 900 2100 1400 1800 1900 1000 1800 1700 2100 800 1100 900 1600 1700 1400 1100 1200 1700 900 700 900 ...
0
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1answer
35 views

How to find equation for 11 independent variables that predicts a single outcome?

I don't know a lot of statistics so I don't even know what search terms to use... I have a data set that includes 11 independent variables. All quantifiable, like age, height, weight, IQ, etc. that ...
2
votes
1answer
27 views

What is the variance of a Polya Gamma distribution?

I have a simple application that needs the variance of a Polya Gamma distribution (I know the mean since I found it here- http://arxiv.org/abs/1205.0310). This paper says that there is a closed form ...
0
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0answers
13 views

Markov Chain to generate random Words

I would like to generate 1000 words (for example) using a Markov matrix of alphabets probabilities. It will be helpful if Matlab code provided. ...
1
vote
0answers
31 views

What is the distribution of the difference between two Gamma's? [duplicate]

Suppose $X$ is $\text{Gamma} \sim (2,.5)$ and $Y$ is $\text{Gamma} \sim (2,.5)$ and $X$ and $Y$ are independent. Let $Z = 1/8(X-Y)$ what is the distribution of $Z$? I know $X+Y \sim (2+2,.5)$ what if ...
0
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0answers
6 views

UMP test for two different distributions

My question: UMP test for H0: X~u(0,1) vs H1: X~Exp(1) My attempt : By nayman pearson lemma The best critical region is Y >= c Where Y has Irwin-Hall distribution (sum of uniform distribution) and c ...
0
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0answers
26 views

What does the Two Stage Experiment Theorem mean

I have been teaching myself statistics out of The Theory of Statistics and Its Applications from Rice(http://www.stat.rice.edu/~dcox/Stat581/chap1-2.pdf) but I'm stuck at one theorem I just can't seem ...
0
votes
1answer
25 views

percentage of reduction and log transformed

I have the following model: log(Y) = Intercept + beta1 * X + Error -> interpretatoion: "One unit increase in X is associated with a (beta1 * 100) percent increase in Y". And now i wish have ...
0
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0answers
31 views

If the sample standard deviation and standard error are biased estimators, why are they still so useful?

The sample standard deviation and standard error of the mean are biased estimators for their corresponding population population parameters. As explained here for the sample standard deviation this is ...
0
votes
1answer
46 views

How to solve this problem on Curse of Dimensionality problem - Nearest Neighbours

I have started learning classification techniques and trying to solve the problems from the book Introduction to Statistical Learning. While currently working on the which is based on Curse of ...
6
votes
2answers
232 views

Can we average over a Cauchy random variable?

Assume $X$ is a standard Cauchy random variable with density $f(x)$, and define a continuous transformation $Z= g(X)$. What happens with $$E(Z) = \int f(x)g(x)dx = ?$$ Does it exist /is finite? Are ...
1
vote
1answer
56 views

Determinant of the covariance matrix in a normal distribution

Suppose a $p \times 1$ vector $x \sim N_p(\boldsymbol 0, \boldsymbol \Sigma_1)$. Now, There is another covariance matrix $\boldsymbol \Sigma_2$. We know that $|\boldsymbol \Sigma_2| < |\boldsymbol ...
0
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0answers
31 views

difference between machine learning and stastitical technique [duplicate]

Is there any difference between machine learning and stastitical techniques. I have searched a lot some researchers say that there are some overlap some are saying there is no difference.Can you give ...
0
votes
0answers
20 views

Transformations in Simple Linear Regression [duplicate]

Suppose a linear model for Y in a single predictor var, X. If the residuals show a pattern of increasing variance (wrt X), sometimes a transformation of Y, Y'=f(Y) is considered (where f is sq rt, ...
1
vote
2answers
57 views

Comparison of machine learning algorithms

Suppose i have taken 8 machine learning algorithm which is used researchers more frequently.I have applied these 8 machine learning algorithm over 8 datasets which is publickly available on internet. ...
3
votes
1answer
28 views

asymptotic distribution of joint random variables

I am trying to understand the asymptotic distribution of the following expression under normality $$ {\hat \sigma \hat S - \sigma S} $$ Where $\sigma$ and $S$ are the population standard deviation ...
7
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0answers
90 views

What Ratio of Independent Distributions gives a Normal Distribution?

The ratio of two independent normal distributions give a Cauchy distribution. The t-distribution is a normal distribution divided by an independent chi-squared distribution. The ratio of two ...
0
votes
0answers
38 views

Request for reference for longitudinal data analysis which is mathematically well-written

I'm a person with graduate level mathematics and some undergraduate statistics background, who'll have to study some basic longitudinal data analysis. I've studied the basics of correlation and ...
0
votes
0answers
28 views

jump in the sign of loglikelihood

I am trying to find the maximum of a loglikelihood function in a two dimensional parameter space__ e.g. X,Y positions are the free parameters__ by making grids in the parameter space and compute the ...
25
votes
7answers
3k views

If 'correlation doesn't imply causation', then if I find a statistically significant correlation, how can I prove the causality?

I understand that correlation is not causation. Suppose we get high correlation between two variables. How do you check if this correlation is actually because of causation? Or,under what conditions, ...
0
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1answer
48 views

Expectations of the geometric mean of a random sample from a uniform distribution

If I have a random sample of size n from a Uniform(0,1) and I define the geometric mean as G can anyone give me insight in to how I can find the expected value of G, E[G]? Once I can get my head ...
0
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0answers
27 views

Do odds increase over exposure time?

Suppose there is 1% chance of death from touching a certain spot on an outlet for 1 second. If one person touches the spot one time per year (1 sec) and second person touches the spot for 1 sec, 12 ...
1
vote
1answer
23 views

Calculating the mean excess loss

Suppose $X$ has the following pdf: $$ f_x(x)=0.01 \qquad for\space 0\le x<100$$ Find the pdf of $X_p$ (the excess-loss variable) and calculate the mean excess loss for $d=10$. \begin{align} ...