1
vote
1answer
41 views

fastest and most efficent way to count all combinations in many sets and sum them together

I am a Java programmer who has reached the limits of brute computer power. My relational database (and non relational databases) is not producing results quick enough and I have hit a bottleneck in ...
2
votes
0answers
249 views

Algebra problem involving Q functions

I have the following algebra problem, which is actually the end-part of my bigger research problem. Let $a$, $b$ and $m$ be reals with $a<b$. Also, let $Q(\cdot)$ denote the Gaussian ...
1
vote
1answer
32 views

Need my data to fit ANOVA…

I am doing some research on constructed wetlands. I have four wetland as follows. Wetland A - Gravels Wetland B - Gravels + Plant Wetland C - Biochar + Plant Wetland D - Biochar + Gravels + Plants ...
0
votes
0answers
31 views

Sum of function applied to parts not equal to function of total

The general goal is to determine the effectiveness of the test pill's ability to keep the test subjects from getting sick using the following data. | Test Subjects | Took Test Pill | ...
0
votes
1answer
39 views

Understanding an equality that involves the gamma function

$$\frac{1}{\sqrt{2\pi}}\sigma^m \Gamma\left(\frac{m+1}{2}\right) 2^{\frac{m+1}{2}} = 2^{\frac{m}{2}}\sigma^m \left(\frac{m-1}{2}\right) \left(\frac{m-3}{2}\right)\cdots \left(\frac{3}{2}\right) ...
0
votes
2answers
33 views

Total boundness of Lipschitz densities

In the article Almost Sure Testability of Classes of Densities by Devroye and Lugosi in 1999. They claim in Example 10 (page 9) that Lipschitz densities on [0,1] with Lipschitz constant bounded by ...
0
votes
1answer
26 views

Question about Logistic Regression - 5

Can somebody give me a clear explanation about logistic regression in bold below? Logistic regression can be binomial or multinomial. Binomial or binary logistic regression deals with situations in ...
1
vote
3answers
35 views

Methods to distinguish continuous probability distributions

I read in the Wikipedia article for Variance The variance is one of several descriptors of a probability distribution. In particular, the variance is one of the moments of a distribution. In that ...
1
vote
0answers
33 views

Bivariate Correlation Unique solution

I have a set of data, let's say "score vs loss ratio", the score is an arbitrary number I gave to a team by looking at their past history. I want to prove my hypothesis which is higher the score, high ...
0
votes
0answers
25 views

What’s the relation between the constraint parameter and penalty parameter in lasso regression?

Lasso regression adds a constraint that ∥β∥1, the L1-norm of the parameter vector, is not greater than a given value (say c). Equivalently, it may solve an unconstrained minimization of the ...
0
votes
0answers
6 views

Doing a confirmative factor analysis for Technology Acceptance Modell

i'm fairly new to statistics an need to check if the TechnologyAcceptanceModel(can be seen here: http://istheory.byu.edu/w/images/9/90/Tam.JPG) fits my data. I extended it by a Factor of Usability. ...
1
vote
0answers
21 views

Logistic regression eye treacting data (need model)

I have two sets of time course data, they are for an eye-tracking study. The data is 20 100ms chunks, one category being percent fixations for canonical sentences, and the other being percent looks ...
1
vote
0answers
33 views

Time series analysis ARCH($m$) model

Consider a stationary ARCH($m$) model $a_t=\sigma_t\epsilon_t$, where $\sigma^2=\alpha_0+\alpha_1a^2_{t-1}+\cdots+\alpha_ma^2_{t-m}$. V. Consider an ARCH(2) model. Write down the predictor of ...
2
votes
1answer
45 views

Calculating the odds of winning a card game

So my friend made this game and I want to the odds of winning his game. So his game is basically I pay \$$1$ to draw $2$ cards from the deck and guess $2$ numbers and one suit. For each correct guess ...
0
votes
0answers
22 views

What analyzation method should be used to prove this thesis?

Good day, I have the following dataset: Name of team | score | role 1 | role 3 Here is some information (And the thesis) There are two teams A and B. The thesis ...
0
votes
1answer
78 views

Derive asymptotic behavior of inverse of the normal cdf with respect to 2^n

I have a normal distribution $\mu = 0$ and $\sigma = 0.58n$ where $n > 0 $ and I am trying to derive the asymptotic behavior of the following equation: ...
0
votes
1answer
70 views

log partition function of exponential family

In an exponential family $$p_{\theta}(x)=\exp \left(h(x)+\sum\limits_{i=1}^s \theta_iT_i(x) - \phi(\theta) \right) $$ is the log partition function $$ \phi(\theta)=\log \int \exp ...
0
votes
1answer
37 views

Raffle Odds and Payout

There are four raffles. One raffle ticket costs $\$500$. Raffle one sells $500$ tickets with winning ticket a payout of $\$80,000$. Second raffle one raffle ticket costs $\$150$ only sells $1,500$ ...
0
votes
1answer
16 views

Using Taylor's series

Using Bayes Theorem I have solved a problem to the equation P(Dc|-) = (0.98-0.98p)/(0.98-0.93p) between the interval [0,0.1]. Show (e.g., by means of Taylor series) that in this interval the P(Dc|−) ...
0
votes
1answer
120 views

Estimating sum of two gaussians using a single gaussian

The problem I have a sum of gaussians: $$ \Sigma(x) = p_1 e^{-\dfrac{1}{2}\left(\dfrac{x-u_1}{s_1}\right)^2} + p_2 e^{-\dfrac{1}{2}\left(\dfrac{x-u_2}{s_2}\right)^2} $$ which I'd like to ...
2
votes
2answers
223 views

Almost sure convergence of a sum of random variables

Suppose $(X_i)_{i=1}^{\infty}$ is an i.i.d. sequence of rv's, where $X_i$ can take countably many values $\{x_1,x_2,\dots\}$ with probabilities $\{p_1,p_2\dots\}$, respectively. Let $p_{n,k}:= ...
5
votes
1answer
116 views

Expected overlap

Suppose I have an interval of length $x$ and I want to drop $n$ sticks of unit length onto it (where $\sqrt x<n<x$). What is the expected overlap between sticks? ($x$ can be assumed to be large ...
1
vote
1answer
76 views

How to apply logistic regression to analyse and predict kind of problem

Say I want to predict whether a new question posted in stack overflow will get an answer within 24 hrs. I was given details about previous questions and all data. Now I have thousands of observations ...
1
vote
1answer
264 views

Difference between Rician distribution and Gaussian distribution

could any one please tell me the difference between Rician and Gaussian Distribution and the advantages of using one over other please.With some mathematical proof would be truly appreciated Thank ...
0
votes
1answer
36 views

Calculating fairness in a competition across offices

We want to run a fitness competition in our company using pedometers to determine which office location is the healthiest. The problem is, we can't use total number of steps, because each office has a ...
1
vote
1answer
350 views

Difficult and unusual probability problem, how to solve?

Let $n_i$ be the $i$'th randomly chosen element from $\mathbb N$ with replacements. All elements have probability greater than zero of being chosen. After a number of trials $k$, the probability ...
6
votes
1answer
940 views

Why are additional constraint and penalty term equivalent in ridge regression?

Tikhonov regularization (or ridge regression) adds a constraint that $\|\beta\|^2$, the $L^2$-norm of the parameter vector, is not greater than a given value (say $c$). Equivalently, it may solve ...
2
votes
2answers
300 views

Upper bound for the absolute value of an inner product

I am trying to prove the inequality $$ \left|\sum\limits_{i=1}^n a_{i}x_{i} \right| \leq \frac{1}{2}(x_{(n)} - x_{(1)}) \sum\limits_{i=1}^n \left| a_{i} \right| \>,$$ where $x_{(n)} = \max_i x_i$ ...
1
vote
0answers
87 views

Compute significance of Kendall tau-b?

I have so-far tried all ways of computing kendall tau significance (where there are ties) described here. However, none of them works good, even for relatively large vectors. I think the problem is ...
3
votes
0answers
47 views

Help with Statistical Analysis

I have been asked to conduct a small survey and then analyse the results of the said survey for a class project. I decided to conduct an anonymous survey of voters for the 2012 presidential elections. ...
0
votes
2answers
54 views

Is there any significant Geometric/analytic property of the Pearson coefficent that could be applied to statistics?

Is there many significant Geometric/analytic property that the Pearson coefficent has which could be applied to statistics? It seems very interesting to me. Thanks in advance.
0
votes
1answer
288 views

Generating a random monotonically increasing polynomial?

Given a polynomial $y : \mathbb{R} \mapsto \mathbb{R}$ of degree $p$: $$ y(x) = \sum_{k=0}^p c_k\, x^k,$$ can a random set of coefficients $\{c_0, \cdots ,c_p\}$ be generated such that $y$ is ...
1
vote
1answer
86 views

Touch Typing Index - Speed and Accuracy

I am trying to determine the ability of my students to touch type. I have data on their speed (in seconds) and their accuracy (number of errors). I also know the number of words in the test (50 ...
1
vote
1answer
2k views

Weighted average vs. weighted mean

Is there a formal difference between weighted average and weighted mean? I get corrected to the latter if I type in the former in wikipedia, and then there is a lot of stuff about the name "average" ...
1
vote
0answers
80 views

Trying to create an algorithm that takes into account multiple variables

I've hit a road block on how I can put what I have into a calculation that works. Simply I am trying to work out the "value" of each company that we have on my companies books. The information I want ...
4
votes
1answer
446 views

Help understanding this formula on mutual information (used in bioinformatics)

I'm a bit lost on understanding this formula in my bioinformatics text, and I appreciate any tips or advice. Mutual Information, $\operatorname{MI}(X; Y)$ is: $$ \mu = \sum_x \sum_y p(xy) ...
2
votes
0answers
168 views

calculate the rate of change

I am trying to calculate the change frequency for a set of data. Each bit of data has the date-time it was created. I would like to say for a specific set of data the change frequency is hourly, ...
2
votes
2answers
194 views

Formula to generate a score from 1 to 100 based on 2 percentages?

I am trying to come up with a formula that will result in a score of 1 to 100 (never anything lower or higher). I have two numbers that I can use to come up with this score, a specific percent and an ...
0
votes
1answer
53 views

How can I calculate max value, if I know just number of records, minimal value and average value of all records?

How can I calculate max value or all possible and relevant maximum values, if I know number of records, minimal value and average value of all records? For example: Number of records (persons): 92 ...
1
vote
2answers
209 views

dividing samples in equal slabs

I have sample data like in above format along X, Y axis. Now what i would like to do is to devide it in "n" number of slabs having fixed values. Now how do i achive this in mathematics(statistics). ...
8
votes
1answer
421 views

Monotonic behavior of a function

I have the following problem related to a statistics question: Prove that the function defined for $x\ge 1, y\ge 1$, ...
0
votes
1answer
30 views

File Size Stats

This is kind of a programming question, but really it's math in disguise! I'm working on a little project that will look at the size of a file and make sure it's in within an acceptable range based ...
1
vote
1answer
86 views

Spread evenly $x$ black balls among a total of $2^n$ balls

Suppose you want to line up $2^n$ balls of which $x$ are black the rest are white. Find a general method to do this so that the black balls are as dispersed as possible, assuming that the pattern ...
1
vote
0answers
65 views

MinimizeVarianceIntuitively function or approach needed

We have a problem the arises in asset management. I think (and hope) it raises interesting enough questions for this forum to consider it. We made pretty extensive searches of the literature and ...
2
votes
1answer
109 views

Efficient Sampling

I'm trying to sample a lot of points efficiently. I'm wondering if the following method is possible. I sample points of a function (evaluate the function) mod $n$. I.e. I calculate f(element one), ...
4
votes
0answers
161 views

Critical exponents and point-wise convergence

A phase change is only possible in a physical system which obeys the laws of statistical mechanics if the infinite series for the partition function of that system converges non-uniformly (i.e. ...