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.

learn more… | top users | synonyms

1
vote
0answers
32 views

Determining the Cramer-Rao lower bound

Let $X = (X_1,\dots,X_n)$ be a vector of iid variables from the smooth density $f(x,\theta_0), \theta_0 \in \Theta \subset \mathbb{R}$. Let $L(\theta)$ be the likelihood and $I(\theta)$ the ...
0
votes
1answer
20 views

Compound Interest - Initial Amount Borrowed [closed]

Could someone explain how to calculate this question? Two loans of an equal amount were taken out at $10\%$ interest per annum for $3$ years and $4$ years respectively. The difference in the ...
1
vote
1answer
14 views

Avg # of Rectangle Intersections in 2D Field

So imagine I have a large 2D field. Thousands of small rectangles overlay the field. The field is much larger than the rectangles. The rectangles are placed randomly in the field such that they may or ...
0
votes
0answers
33 views

Estimators of the binomial distribution

This is a follow-up of this previous question and elaborates on the answer I received there. $\def\b{\begin{pmatrix}}\def\e{\end{pmatrix}}\def\a{\alpha}X_1,X_2,\dots, X_n$ are a random sample from ...
1
vote
1answer
27 views

How to predict next number from a given set of measurement data?

I have to do some experiment and measure it on a specific time 0, 3, 6, 9, 12, 18, 24, 36 months $$ \begin{array}{l|c|c|c|c|c|c} \text{Month} &ID1 & ID2 & ID3 & ID4 & ...
1
vote
1answer
31 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
1answer
28 views

How to estimate the standard deviation in this normal distribution?

There is this simple looking basic statistics question that asks to estimate its mean and standard deviation. I have some doubts and just want to make sure whether my working is correct. For part ...
0
votes
1answer
20 views

Standard deviation in normal distribution

A manufacturer uses a machine to make metal rods.The diameter of the rods follow a normal distribution with a mean of 1cm and a standard deviation of 0.02cm If the standard deviation of the diameters ...
0
votes
0answers
10 views

find the mean of a collection of the solutions of given linear systems

Suppose one has a group of $k\times k$ square matrices $A_i, i = 1,2..n$, another $k$-vector $b$ is also given. I want to exam the mean of the group of vectors $x_i$ over $i = 1,2...n$ where $A_i * ...
1
vote
1answer
19 views

Simplify $\dfrac {\partial }{\partial b}\left( \sigma ^{2}\right) =0$ and $\dfrac {\partial }{\partial m}\left( \sigma ^{2}\right) =0$

Given $\sigma ^{2}=\sum ^{N}_{i=1}\left[ y_{i}-\left( mx_{i}+b\right) \right] ^{2}$ How to simplify $\dfrac {\partial }{\partial b}\left( \sigma ^{2}\right) =0$ and $\dfrac {\partial }{\partial ...
0
votes
0answers
20 views

Negative integer factorial in Koziol's combinatorial approach

I' m trying implement Unbiased split selection from this document: http://www.stat.uni-muenchen.de/sfb386/papers/dsp/paper464.pdf I have problem on 14 page. I have list of $$ \binom{i_k}{j_k} $$ $$ ...
0
votes
1answer
13 views

Finding the percentile of a value given other percentiles

I am using someone else's research and only have part of the data. I want to find the percentile of a value, such as 350.2, based upon the data given. The following is known: mean = 308.2 The ...
2
votes
2answers
13 views

How to prove a given statistical test has the greatest power

It is very conventional in evaluating the null hypothesis to consider the distribution of the mean of a sample of some size if the null hypothesis were true and to compare the mean of your own sample ...
0
votes
0answers
13 views

Comparision between Hamming distance and cosine similarities?

I want to check the similarities between binary vectors of different length and I am using cosine similarities and hamming distances for calculations. These are of length 1000 elements(0 and 1). ...
1
vote
1answer
21 views

Median of grouped data

part (ii) Median = $Lm +(n/2-cf)/fm*h$ = $171+(20-16)/12*3$ = $172$ am i correct?
0
votes
1answer
30 views

Statistical Inference - Finite Population Correction

I am studying for an exam in Quantitative Analysis and I am looking through past exam papers (here's a link the exercise I'm referring to: http://i62.tinypic.com/2cz1nqh.jpg). I understand all of the ...
0
votes
1answer
27 views

Equivalence of two formulas for variance and covariance

I know two formulas for variance: $$\operatorname{variance}(f) = \operatorname{expectation}((f(x) - \operatorname{expectation}(f^2(x)) \\ = \operatorname{expectation}(f(x)^2) - ...
0
votes
1answer
26 views

How to derive “Pooled Sample Variance”?

Let $s_p^2 = bs_1^2 + (1-b)s_2^2$, this can be an unbiased estimator of population variance, provided we find the correct value for $b$; in particular, $s_p^2 = \frac{(n1-1)s_1^2 + ...
1
vote
1answer
41 views

Statistics Probability Density Functions with Mutliple Features (Multivariate Normal Distribution)

I'm looking for a beginner-friendly explanation on how this Probability Density function works when dealing with mutliple features and what the variables and terms mean in detail. I'm seriously ...
1
vote
1answer
32 views

A Bayesian estimate for rank

I am not sure how to put this succinctly but here is the problem. Consider a random variable $X$ which can take a finite number of non-negative values. It takes each value with the same probability. ...
1
vote
3answers
58 views

Derivation of standard error of mean

I was going through this wikipedia article on standard error. I could not understand the crucial step here. It goes like this: This formula may be derived from what we know about the variance of a ...
3
votes
2answers
62 views

Does an exponential model fit my data?

I am measuring accumulation of a fluorescent-tagged protein at a particular location within a cell over time. In previous experiments that I have performed, I see a standard exponential distribution ...
1
vote
1answer
27 views

time series similarity heuristic

What is a good heuristic for time series similarity. I'm ok with false positives bc I will then pass the results of the heuristic to an actual series similarity algo. Basically I want the heuristic to ...
2
votes
1answer
59 views

Math required for medical statistics

I have never been good with Math. I talk to many of my medical colleagues and it seems to me that most of them have a poor understanding of statistics. Many of them claim to understand it but actually ...
0
votes
1answer
21 views

How to calculate lower & upper quartiles?

I'm sure this has been asked many times before but it's confusing me a lot so hopefully someone can help! I am given this data set: 0.28 0.30 0.42 0.59 0.71 1.67 1.82 2.39 4.71 4.79 4.89 5.00 5.00 ...
3
votes
2answers
81 views

How to give rigorous proofs of these two limit statements?

Let $X$ be a random variable with cumulative distribution function $F(x)$. Then how to rigorously prove the following two limit statements? $\lim_{x \to - \infty} F(x) = 0$. $\lim_{x \to + \infty} ...
-1
votes
1answer
31 views

Why the standard deviation approximated by the range rule of thumb much different from the standard deviation calculated directly from sample data?

What makes the standard deviation approximated by the range rule of thumb much different from the standard deviation calculated directly from sample data? For example, if the approximate standard ...
0
votes
0answers
37 views

Outliers in a Normal Distribution

Im doing AP Stat. in High School level. Here is a question i am stumped on because i feel like it is maybe a threory or law or something that i just never learned. However it DOES ask to show my ...
1
vote
1answer
23 views

Finding moment estimator

I am required for a homework question to find moment and maximum likelihood estimators, and in class we have only looked at finding MLEs and using already known moment estimators, hence I have no idea ...
1
vote
1answer
25 views

Find the Distribution of an Order Statistic

I am working on a practice prelim question. It states: Let $Y_1 < Y_2 < Y_3 < Y_4$ denote the order statistics of a random sample of size 4 from a distribution which is uniform on ...
0
votes
1answer
30 views

Interpretation of a statistical formula involving the ratios of sample and population

Kind of an odd question, but, is this a standard equation for stats? I can't figure out for the life of me what it looks like. $\left(\frac{\text{Sample Of A}}{\text{Population Of ...
1
vote
1answer
21 views

Calculating expectation and using the delta method

Let $\hat{p}$ be the proportion of successes in $n$ independent Bernoulli trials each having probability $p$ of success. (a) Compute the expectation of $\hat{p} (1-\hat{p})$. Isn't $P(\hat{p} = k) = ...
0
votes
1answer
9 views

Derivation of Mode of grouped data

A formula to calculate the mode for grouped data's is given in my text book: Mode = $l +$ $ (f_1 - f_0) \over (2f_1 - f_0 - f_2) $ $ * \ h $ Where, $l = $ lower limit of the modal class, ...
1
vote
1answer
34 views

A Bayesian estimate of the bias of a coin

Consider a coin with unknown probability $p$ of landing on head. I will toss the coin and stop as soon as I get a head. Say this is after $n$ tosses. If my prior belief for $p$ was uniform on ...
0
votes
1answer
25 views

$|p- \dfrac xn|>|q- \dfrac xn|$ $\implies$ $p^x(1-p)^{n-x}<q^x(1-q)^{n-x}$?

If $p,q \in (0,1)$ , and $ n \in \mathbb N$ be given and $x$ be given integer between $0$ and $n$ such that $|p- \dfrac xn|>|q- \dfrac xn|$ , then is it true that ...
0
votes
1answer
27 views

Estimator with smallest variance, Lagrange multiplier

I have a question and I think I'm supposed to use the Lagrange multiplier although I haven't been taught it, so I'm not sure if I can use it or not. The question is: Suppose that $X_i$ has mean $\mu$ ...
1
vote
1answer
10 views

Showing deviation of data on a fixed scale

I'm creating a chart in D3 which shows the Mode from a large (1mil +) dataset; and colors it according to the standard deviation of the dataset. But the issue is that I need to map the range (Red ...
0
votes
1answer
59 views

Maximum likelihood estimators

I have $X_1,X_2,\dots,X_n$ as random samples from a binomial distribution, with probability function: $$p_X(x) = Pr(X=x) = {m \choose{n}}\alpha^x(1-\alpha)^{m-x},x=0,1,2,\dots,m$$ where $m$ is given ...
0
votes
0answers
15 views

Expectation Maximization Algorithm for Gaussian Mixture Model

Can we use the Expectation Maximization algorithm for estimation of Gaussian Mixture Model with full covariance matrices? If yes then can you please give me a reference paper? So far all the machine ...
1
vote
4answers
85 views

Estimate bias of a coin

Consider a coin with probability $p$ of landing on head. You can estimate the prob by tossing it lots of times and looking at the proportion of heads one gets. In my problem I just want to know if ...
0
votes
1answer
35 views

Is Inverse Standard Normal Distribution $\Phi^{-1}(x)$ related to $erf^{-1}(x)$?

I am looking to use $normsinv$ to implement $inverf$ in a spreadsheet. Cumulative Standard Normal Distribution, $\Phi$, is related to $\mathrm{erf}$: $\Phi(x) = {1 \over ...
0
votes
0answers
16 views

An example of $k$-independent distributions.

I'm trying to better understand the idea of $k$-independence in distributions. The idea is that a distribution $\mu$ over $\{0,1\}^n$ is $k$-independent if any restriction of $\mu$ to $k$ variables ...
0
votes
0answers
33 views

Proof that data-processing selection process is statistically independent of the sample?

I hope to replace a proof of my own, in a paper explaining that the "no free lunch" theorems for optimization actually address sampling and statistics, with a reference to an existing result on ...
0
votes
0answers
21 views

Calculating close to a uniform distribution where the mean is different then the midpoint?

I need some help understanding what type of distribution calculation I need. I am attempting to achieve as close to a uniform distribution as possible, but subject to the constraint that the mean of ...
0
votes
0answers
8 views

Two stage GMM estimator in Matlab

I am trying to create a simple GMM estimator for the mean of a normally distributed random variable using the first three odd central moments of a normal distribution (all of which should be zero ...
0
votes
0answers
14 views

Check work for finding Max log-Likelihood of a geometric Distribution

Here is my geometric distribution: $P(L=n)=p^{n}*(1-p)$ To find the max likelihood, I do: $\sum_{L_i} L_i\log(p) + \log(1-p)$, where L_i is a particular length. I take the derivatives and end up ...
0
votes
0answers
24 views

Notation for parametric family of joint densities

This is copied from my textbook; Assume that the statistical model for the MVR $\textbf{Y}=(Y_{1},Y_{2},\ldots , Y_{n})^{T}$ is given by the parametric family of joint densities: $$\{ ...
1
vote
1answer
51 views

Measure dispersion of a set of values resides in a range

I want to know what is best method to calculate (measure) the statistical dispersion of a set of values resides between a range. Scenario: My goal is to build an index. I have two methods that ...
1
vote
1answer
35 views

probability of bingo

It is the first time I heard about bingo game and I would like to learn more on this game by mathematical analysis. To make it simple, I consider the American BINGO with 75 balls used and each game ...
0
votes
0answers
19 views

The use of Weighted arithmetic mean to determine the extent to which the data correspond

I don't know when I can ask such question, because it is not a completely mathematic question. I have a text and a topic (single word). I want to check how much this text corresponds to the topic. ...