Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis.

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222 views

MCMC Metropolis Hastings

Does anyone know a webpage or a document where I can find a practical example of implementation of the Metropolis-Hastings algorithm, with some thoughts about burn-in time and how to construct the ...
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1answer
325 views

bayesian networks for regression

Would it be possible to use bayesian network for regression and/or prediction? I understand that it is a tool one can use to compute probabilities, but I haven't found much material about possible ...
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1answer
4k views

Interquartile range

I have grouped data ranges that I need to find the interquartile range for, I think i have found the groups that the upper and lower quartiles are in, but as they are ranged, where do I go from here? ...
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1answer
4k views

How can I calculate the standard deviation knowing an event probability and a number of trials?

I'm writing a test for a probabilistic data structure that I've implemented. Since its probabilistic, its performance is different every time, and in particular, the performance varies much more ...
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1answer
102 views

estimation of pdf

when estimating a probability distribution function one may, for instance, gather a set of data and use the hist function in Matlab to get an idea of what's the pdf like. My question is this: if you ...
2
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2answers
152 views

If $X$ is uniformly distributed on $ [0,1]$, how is $X^2$ distributed?

I seem to be getting it equal to the $X$, which can't be right
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1answer
96 views

Calculate probability given double outcomes

An event may result in A, B or C. The probability that the result is A or B is 96.1% The probability that the result is A or C is 84.0% The probability that the result is B or C is 33.3% What is ...
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3answers
458 views

Fast computation/estimation of the nuclear norm of a matrix

The nuclear norm of a matrix is defined as the sum of its singular values, as given by the Singular Value Decomposition of the matrix itself. It is of central importance in Signal Processing and ...
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3answers
830 views

Is it wrong to use Binary Vector data in Cosine Similarity?

I am doing Information Retrieval using Cosine Similarity. My data is binary vector. Since most of all reference I read is using non-binary vector (non-binary matrix) data, I am wondering if it is ...
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2answers
415 views

Calculate Line Of Best Fit Using Exponential Weighting?

I know how to calculate a line of best fit with a set of data. I want to be able to exponentially weight the data that is more recent so that the more recent data has a greater effect on the line. ...
3
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1answer
505 views

Single number to represent a ratio?

There's probably a very simple answer to this, but I can't put my finger on it. I have two numbers. I want one to be large, and the other to be small. I'd like to identify these with a single ...
2
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1answer
227 views

Likelihood Function

How do we write the likelihood function of a problem that consists of more than one x variable? (In my case it is x1, x2 and x3)
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2answers
220 views

Average, exponential moving average, identities/splitting input parts

I would like to know if certain identities for averages (mean) also hold for the exponential moving average (EMA). I can verify the mean case, but not the exponential case. Can somebody tell me if the ...
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4answers
2k views

How can I calculate “most popular” more accurately?

I'm developing a website at the moment. The website allows users to "rate" a post from 0 to 5. Posts can then be displayed in order of popularity. At the moment, my method of calculation is pretty ...
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2answers
262 views

Probability of achieving a given density of IID random variables

I have a sequence of IID random variables $X_1, X_2, \dots, X_n$. In this particular case, each of the variables is Lévy distributed with PDF $f(x) = (\lambda / 2 \pi x^3)^{-1/2} \exp(-\lambda/2x)$ ...
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1answer
330 views

Recursive coefficient of determination (R2)

Is there a way to compute the coefficient of determination $R^2$ in a recursive way? $R^2$ is defined as following: $$R^2 \equiv 1 - \frac{SS_{\rm err} }{ SS_{\rm tot}} = 1 - \frac{\sum_i (y_i - ...
5
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1answer
190 views

Finding the joint distribution of $X_{1:n}$ and $\overline{X}$

I need to show that, given a random sample of independent variables $X_1, ... , X_n$, each following a distribution EXP($\theta$,$\eta$), that is, ...
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1answer
140 views

Function characteristic

I'm using the function $$\frac{xe^{-x^2}}{\int_0^1 te^{-t^2} \, dt}$$ as a probability density function for generating numbers between 0 and 1. If I want to increase the probability to the zero (crush ...
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2answers
9k views

Calculating the variance of the ratio of random variables

I want to calculate $\newcommand{\var}{\mathrm{var}}\var(X/Y)$. I know that the solution is $$\var(X) + \var(Y) - 2 \var(X) \var(Y) \mathrm{corr}(X,Y) \>,$$ but, how do I derive it from "common" ...
4
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1answer
141 views

Showing that $X_{1:n}$ is sufficient for $\eta$, by factorization

I'm asked to show that $X_{1:n}$ (the minimum order statistic) is sufficient for $\eta$, in the case of a random sample $(X_1, ... , X_n)$ where $X_i\sim EXP(1,\eta$) (this is the two-parameter ...
0
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2answers
65 views

Greater precision with regression?

I used my TI-83 to find the quadratic regression of two data columns. The accuracy wasn't close at all. So I tried cubic and then finally quartic regression. The accuracy still isn't close enough. Is ...
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0answers
91 views

Variability of a curve with Vapnik-Chervonenkis dimension 4

Say I have 10,000 data in 2-D and I want to fit a curve to them. There are many functional forms this curve could take -- polynomial, B-spline, trigonometric, and so on. I've decided that I only want ...
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2answers
133 views

Calculating population size at any future time

If current population size is $P$ and average life-time of any member is $L$. Any pair of member of the population is allowed to have $C$ children on an average. They can have children between the age ...
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1answer
57 views

How to express the traditional variogram for a non 2nd order stationary random function?

Consider an intrinsic RF Z(x) that is not second order stationary. Considering an arbitrary reference RV Z(x0), how to express traditional variogram in terms of covariance of increments expressed ...
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1answer
470 views

What is the significance when the inverse covariance matrix = the identity matrix?

The question is self explanatory. I just wish to know the significance of this property of matrices. Thanks
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2answers
619 views

Standard error of the mean for root mean square of data

If I have a distribution of data, X, representing N samples taken during one measurement, then the mean square of X is $\bar{X^2} = \langle X^2 \rangle$, the variance of $X^2$, $\mathrm{var}(X^2)$ is ...
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2answers
754 views

How to work out a Mahalanobis distance

Currently going through my Lecturer's notes and came across the Mahalanobis distance but nothing in the notes on how to work this out and googling hasn't really turned up anything either. My maths ...
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4answers
591 views

What is the deepest / most interesting known connection between Trigonometry and Statistics?

I'm teaching both at the same time to different classes in high school, so I just wondered about this. Added by OP on 16.May.2011 (Beijing time) I mean Statistics only, without Probability. In ...
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1answer
2k views

Combinations and Permutations Question

I am sitting my A level exams (MEI) and I was looking through the S1 past papers and I encountered this question in the January 2010 paper: Three prizes, one for English, one for French and one ...
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1answer
246 views

Relative Entropy given two non-equivalent sets

I am trying to calculate the relative entropy given two collections and have a question regarding some issues. Supposed we have two sets, $Real$ and $Calculated$, and their respective probability ...
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3answers
301 views

Efficient computation of $E\left[\frac{1}{1+\sum_iX_i}\right]$ where $X_i$ is RV with Bernoulli distribution with different probabilities

Suppose we have the random variables $X_1, \ldots, X_n$ that have Bernoulli distributions with the (possibly different) probabilities $p_1, \ldots, p_n$. For example, $X_1$ = 1 with probability $p_1$ ...
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1answer
782 views

Expected value of sum of fractions

Suppose $r$ is a set of attributes with probabilities while $p$ is a set of attributes without probabilities. For example, say that $r$ = {$a$:0.4, $b$:1.0} and $p$ = {$a$, $c$}. (Here, $a.prob = 0.4$ ...
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2answers
138 views

Please solve for X

I messed up the equation last time I asked this - Can someone please solve this function for X? $Y = \displaystyle 0.5\:a\:\text{erf}\left(\frac{x-b}{c\sqrt{2}}+.5\right)+d$ When I solve for Y with ...
3
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1answer
152 views

Finding the population size from the common elements of multiple samples

A coworker of mine has taken a certification exam twice and has seen the same ten questions on both exams. I am curious if it is possible to determine the total number of questions in the question ...
2
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1answer
533 views

Gaussian approximation of Poisson distribution

I am using a Gaussian distribution to generate a Poisson variable with parameter $\lambda$. According to Wikipedia, when $\lambda > 1000$ this approximation is pretty good. However, using MATLAB I ...
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2answers
1k views

How can I solve this equation (contains error function)?

Edited out incorrect formula Can someone please solve this equation for x? I have no idea what to do with the $\mathrm{erf}$ (error function). Edit: Hm, it did not work correctly... here is the ...
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1answer
371 views

Intuitive explanation of Fisher Information and Cramer-Rao bound [closed]

I am not comfortable with Fisher information, what it measures and how and how is it helpful. Also it's relationship with the Cramer-Rao bound is not apparent to me. Can someone please give an ...
30
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2answers
4k views

Why is the error function defined as it is?

$\newcommand{\erf}{\operatorname{erf}}$ This may be a very naïve question, but here goes. The error function $\erf$ is defined by $$\erf(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2}dt.$$ Of ...
4
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1answer
918 views

Fisher Information of a function of a parameter

Suppose that $X$ is a random variable for which the p.d.f. or the p.f. is $f(x|\theta)$, where the value of the parameter $\theta$ is unknown but must lie in an open interval $\Omega$. Let ...
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1answer
421 views

Find probability given frequency for event

Lets say we have three channels with probability of gender based view like this: chA->men = 0.3 chB->men = 0.7 chC->men = 0.8 In a week sample,a user views total 1000 impressions. Out of which ...
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2answers
2k views

Why add 0.5 to a z-score?

Can anyone explain when should I add 0.5 to the z-score?
0
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1answer
261 views

Find angle at which two lines cross

Considering the following dataset, how do I find the angle when the two lines intersect at time 4. Please not that the two lines don't represent a function, this is just a data set. ...
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1answer
55 views

Transform the sample to make it more similar to a given

$X=\{x_{i}\}$ and $Y=\{y_{i}\}$ are numeric samples: $y_i \ge 0, x_i \ge 0, i \in [0..N]$. I need to find the mapping $F(X)=\{F(x_i)\}$ with fairly simple formula such that: Euclidean distance ...
2
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3answers
3k views

Calculating mean and standard deviation of very large sample sizes

I have about 3.5GB worth of data that I need to get statistics from, all split up into about 71MB files, with an (approximately) equal number of samples. From this data, I would like to gather mean ...
4
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0answers
440 views

Chi Squared Distribution for Maximum Likelihood

I'm beginning to work in bioinformatics and have come across some papers that utilize chi-squared distributions to make a maximum likelihood selection. Particularly in the area using 'amplicons'. I've ...
2
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1answer
405 views

Integral with analytical solution with normal distribution

I received very good answers a couple of days ago in a simpler related problem, see Integral with Normal Distributions, but I am struggling with this new question: Let's define a function ...
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2answers
1k views

Stats 101 - Exam Question Fail, or just tricky to answer?

This appeared on a friends Stats 101 exam: You have a random sample of 2000 respondents who's mean age is 47.3. A friend of yours, (who is knowledgeable about such things) claims that ...
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2answers
96 views

Estimating sample size

I have 5 different options(a,b,c,d,e) out of which one is correct(c). What should be the sample size(the number of person i should ask to answer) so that i can get 80% confidence the correct answer(c) ...
0
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1answer
125 views

Kernel Density Estimation

Could someone please help me understand this KDE equation by working out an example? $$=\frac{1}{n*h}\sum_{i=1}^{n} K(\frac{x - x_i}{h})$$ say, for example, I have the data for the following: $$ x = ...