Questions tagged [means]

In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. For a data set, refers to a central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values.

Filter by
Sorted by
Tagged with
0 votes
0 answers
18 views

Recalculate average based on subset of poisson distribution

Assuming a series of independent events, probability of the event occurring on a given day is a poisson distribution with λ=0.8. This includes probability of event ...
user avatar
  • 145
6 votes
1 answer
136 views

Is there a term for abelian groups in which you can divide by natural numbers?

Is there a specific term for an abelian group (or ring) $G$ that satisfies the following property? For every element $g \in G$ and natural number $n$, there exists a $q \in G$ such that $\underbrace{...
user avatar
  • 5,401
-1 votes
0 answers
14 views

calculate the mean angle between four vectors [closed]

what I am trying to to is calculate the mean angle of four normal vectors. For 2 vectors, this seems trivial. But how would i do that for 4? Thanks in advance!
user avatar
3 votes
1 answer
35 views

Identric mean is less than arithmetic mean

I'm doing a paper work about theory of means and their inequalities and I'm trying to prove that if A denotes the arithmetic mean and I the identric mean then $$ I(x, y) \le A(x, y) $$ for $x,y>0$,...
user avatar
  • 33
0 votes
1 answer
30 views

How to show that $\sum_{i=1}^n\left(x_i^2 - \bar{x}^2\right) = \sum_{i=1}^n\left(x_i - \bar{x}\right)^2$

I am reading through a book on linear regression and I am confused as to how a derivation has been done. The derivation up to where I have got is below. $$ \sum_{i=1}^nx_i^2 - \frac{\left(\sum_{i=1}^...
user avatar
0 votes
0 answers
11 views

What does it mean to find the mean vector using simple returns

What does it mean to find the mean vector using simple returns from five selected stocks? I have chosen five stocks and collected their (weekly) data over a 10-year period. And then I have used that ...
user avatar
  • 87
-1 votes
0 answers
26 views

Method of Maximum Likelihood Estimation

I have this continuous function $$f(x)=(ae^ax)/(e^ax+1)^2, \text{ for} -∞≤x≤∞. $$ And I got this log function I tried the following code in Mathematica n = Length[c]; logL = nLog[a] + Total[Log[...
user avatar
0 votes
0 answers
11 views

Weighted least squares as a weighted mean

Imagine I have my datas $\left(\phi_i\right)$ on a 3D regular grid $\left(x_i,y_i,z_i\right)$ [$n$ values with $8 \leq n \leq 40$ in general] and I want to know $\phi_{v}$ at a virtual point $\left(...
user avatar
  • 6,813
0 votes
0 answers
19 views

Deriving the mean of truncated $t$ distribution

I am trying to derive the mean of right truncated $t$-distribution but cannot solve the integration further. I tried to find the truncated mean as follow: The pdf of right truncated distribution is; $\...
user avatar
0 votes
0 answers
13 views

Robust Estimation of Location Parameter. P. J. Huber. (1964).

In the aforementioned book there is a statement: (i) Supremum of the actual variance is infinite for any estimator whose value is always contained in convex hull of the observations. If we take a ...
user avatar
-1 votes
2 answers
29 views

Multiply mean values

I was wondering if its allowed to multiply two mean values. I thought of the following: $$y = x_1 * x_2$$ They values $x_1$ and $x_2$ are from different sample sets and are not related. They only have ...
user avatar
  • 101
0 votes
1 answer
77 views

On the arithmetic-geometric-harmonic inequality [closed]

Im doing some research as a final project for my mathematics degree in the university and I can not find a proof of the following inequality, involving Theory of Means, could someone do it? If A is ...
user avatar
  • 19
1 vote
1 answer
59 views

Is the difference of random walk a martingale

Suppose $X_i \sim i.i.d. N(0,1), i=1,...$, $S_n=X_1+...+X_n$ let's $ Y_{i}^{\left( v \right)} := X_i \textbf{1}_{ \left\{ \left| X_i \right| \leq v \right\} }, X_{i}^{\left( v \right)} := \left( Y_{i}...
user avatar
  • 25
2 votes
2 answers
69 views

Why are mean, median, and mode called central tendency?

Is there any difference between the two terms "Central tendency" and "representative values"? Why are mean, median, and mode called central tendency or representative values?
user avatar
  • 49
0 votes
0 answers
18 views

the mean and standard deviation aren't the same as those of the input data i provided after sampling

have a log-normal mean and a standard deviation. after i converted them to the underlying normal distribution's parameters mu and sigma, I sampled from the log-normal distribution however when i take ...
user avatar
0 votes
1 answer
45 views

Problem about finding the percentages of men and women working at a company according to their average salaries

I am stuck on this problem on the topic of statistics because I don't understand how these kinds of problems are solved. If someone could explain it to me that would be a great help. The average ...
user avatar
0 votes
1 answer
27 views

Finding mean of normal distribution given probability between two endpoints

There is a well-known method for finding the mean of a normal distribution (given its variance) given the probability below a certain endpoint by normalizing the distribution: $$X \sim N(\mu, \sigma^2)...
user avatar
  • 3
6 votes
1 answer
83 views

Inequality help: $\frac{a+b+c}{3}\geq\sqrt{\frac{ab+bc+ca}{3}}\geq\sqrt[3]{abc}$

I'm working through "Calculus of One Variable" by Joseph Kitchen, and this inequality (problem 3 from section 1.3) is causing me quite a bit of pain to prove: $$\frac{a+b+c}{3}\geq\sqrt{\...
user avatar
  • 61
1 vote
0 answers
49 views

How to get an "average" of a distribution with no average

Modelling something where I need some sort of average time, I reached Pareto Distribution, and the PDF is $$ R(t)=\begin{cases}\sqrt{\frac{1}{2\pi t^{3}}}, & \text{for } t > \frac{2}{\pi}\\ 0 &...
user avatar
  • 750
0 votes
1 answer
53 views

Triangle of Fibonacci

I was reading in a book a presentation about the arithmetic triangle of Fibonacci (to me it also looks like the pascal triangle). The figure presented is as follows: The text says: Having arranged ...
user avatar
  • 1,519
1 vote
0 answers
21 views

Positive random variables with harmonic mean equal to mean have variance zero

Suppose $X>0$ is a random variable with $\mathbb{E}X=c$ and $\mathbb{E}X^{-1}=c^{-1}$. By applying Cauchy-Schwarz to $\sqrt{X}$ and $\sqrt{X^{-1}}$ and using the "equality iff linearly ...
user avatar
  • 627
3 votes
1 answer
91 views

Mean of a normalized product of densities

Consider two unimodal probability density functions $ f(x)$ and $ g(x)$ on $\mathbb{R}$, both symmetric around their modes $\mu_f$ and $\mu_g$ which are also their means and medians. Given the ...
user avatar
  • 31
0 votes
1 answer
27 views

MLE of the Geometric Distribution

Suppose that $X_{1},X_{2},...,X_{n}$ are independently and identically distributed as $Ge(\theta)$. (i) Find the maximum likelihood estimator of $\theta$ My solution: $\theta = \frac{n}{\sum_{i=1}^{n}...
user avatar
0 votes
0 answers
19 views

Standard Deviation and data set increasing by multiplication.

Hi guys I recently started learning statistics and I'm a bit confused. I know when a data set is multiplied by a constant, its standard deviation and mean is multiplied by the same number. However ...
user avatar
  • 53
0 votes
0 answers
35 views

Choosing the correct t test for comparing two sample means

Six sets of identical twins were divided at random into two groups, each group containing one twin from each set. The first group was taught some basic statistics by method A and the second by method ...
user avatar
0 votes
1 answer
31 views

Expectation Value and Variance

I know the formula for Expectation value is $$E(X)=\sum f_ix_i$$ where $f_i$ denotes the PMF(Probability Mass Function) and Variance is $Var(X)=E((X-m)^2)$ where m is E(X). But what is really the ...
user avatar
0 votes
1 answer
114 views

Geometric mean with negative numbers

I want a workaround for the geometric mean when the data contains negative numbers. I found this on Wikipedia, but it doesn't work if m is odd and there is an even number of data points. What should ...
user avatar
  • 281
0 votes
1 answer
28 views

A Hypergeometric probability distribution and Zeilberger

On page 107 of book 'The Concrete Tetrahedron' by Manuel Kauers . Peter Paule A Hypergeometric probability distribution is given : consider an urn containing N balls, m green ones and $N - m$ blue ...
user avatar
2 votes
1 answer
83 views

What are the geometric, harmonic, and quadratic averages of a function?

In Mean of a function, they describe the arithmetic mean of a function and at the bottom of the article they said: There is also a harmonic average of functions and a quadratic average (or root mean ...
user avatar
  • 23
0 votes
0 answers
53 views

Sample Mean vs. Population Mean

I'm having trouble understanding what exactly is meant to be found given the information presented. Obviously, the answer will be a value found on the z-table and the probability of this event ...
user avatar
1 vote
1 answer
58 views

Maximization of $\sum (\mu_i - \bar{\mu})^2$

Suppose I have $n$ integers $\mu_i$ , $i=\{1,2,...,n\}$. Define $\bar{\mu}=\frac{1}{n}\sum_{i=1}^{n} \mu_i$. It is given that all the $\mu_i$'s are either $+1$ or $-1$. How can I show that $\sum_{i=1}^...
user avatar
0 votes
1 answer
37 views

Derivation of Inequality of arithmetic and geometric means using a circle

$$a,b:=\text{positive numbers}\tag{1}$$ I want to derive the following inequality. $$\underbrace{\sqrt{ab}\leq{a+b\over 2}}_{\text{Inequality of arithmetic and geometric mean}}\tag{2}$$ To derive it, ...
user avatar
0 votes
1 answer
38 views

Statistics test question about a mean

The following question from a Statistics test does not make sense to me. Question: Data from the past 100 years show that rainfall during April varies randomly from day to day. Over that period the ...
user avatar
  • 203
0 votes
1 answer
32 views

Is the geometric mean bounded above by this value?

It is clear that the geometric mean is bounded above by the arithmetic mean: $$ \prod_{k=1}^{M} x_k^{\alpha_k} \leq \sum_{k=1}^{M}\alpha_k x_k $$ Moreover, it is clear that the arithmetic mean is ...
user avatar
  • 507
0 votes
0 answers
21 views

Does the population variance equal the variance of a single observation?

According to Wikipedia, the standard error $\sigma^-_x$ of a sample mean can be computed by $\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the standard deviation of a statistical population and $n$ is ...
user avatar
  • 1
1 vote
0 answers
30 views

What is the notation for the mean of $y$ in the $i$-th quantile of $x$?

I would like to add the appropriate mathematical notation to use in a figure. I have two original quantitative variables, $y$ and $x$, named “long variable name $y$” and “long variable name $x$”. I ...
user avatar
1 vote
0 answers
27 views

Standard error of the mean for different experiments

I am confused about the calculation of the SEM when one performs multiple independent experiments. Suppose we perform $k$ different experiments obtaining means $\mu_k$, standard deviations' $\sigma_k$ ...
user avatar
  • 11
0 votes
0 answers
25 views

Obtain standard deviation from sum of values

I'm looking for a way to obtain the "composed" mean and standard deviation of two (related) datasets. So let's assume I have n = 25 recordings of one characteristic (x) and the same number ...
user avatar
0 votes
0 answers
25 views

standard deviations for mean vs for predictions

I work in finance and wanted to ask a quick question regarding standard deviation of data sets. I have collected data sets over the last 10 years and would like to use them to make a prediction for ...
user avatar
0 votes
0 answers
24 views

Is this a Mean? Recognizing functional form of a generalized mean.

Can the operator \begin{equation} (f')^{-1}\left(\frac{f(y)-f(x)}{y-x}\right) \end{equation} be interpreted as a mean and if so, does it have a name? If $f(x)=x^2$ then this simplifies to \begin{...
user avatar
  • 1
1 vote
0 answers
24 views

Can we use power mean to generalize min and max for complex numbers?

Power mean $M_p(a,b)$ of order $p \in \mathbb{R}$ for a pair $(a,b) \in \mathbb{R}^+$ is defined as $M_p(a,b)= \Big(\frac{a^p+b^p}{2}\Big)^{\frac{1}{p}}$. For example $p = 1$ gives arithmetic mean, ...
user avatar
  • 98
0 votes
0 answers
10 views

Calculating $Cov\left(\overline{Y}_j,\:\overline{Y}\right)$ for a basic one-way model

Consider the basic one-way model: I want to show that $Cov\left(\overline{Y}_j,\:\overline{Y}\right)=\frac{\sigma ^2}{na}$. I derived the following expected values: $$E\left(\overline{Y}_j\right)=\mu ...
user avatar
0 votes
0 answers
13 views

What test to use to see the difference between two groupps with the same variance?

I have the data for 3 groups A,B,C with the times of run of 5 kilometers. $ \begin{matrix} Group A & Group B & Group C \\ 27.5 & 35.3 & 45.8 \\ 30.6 & 40.2 & 42.6 \\ 28.5 &...
user avatar
0 votes
0 answers
49 views

How to evaluate the difference/distance between 2 values positive and negative on a scale

Problem 1 : The input is 2 values, that can be in a scale between [-3.89, 10.66] And i need to compare the difference between an oldValue (A) and a newValue (B). So i want to create a variable that ...
user avatar
  • 1
0 votes
0 answers
51 views

Sum of deviations from mean and Mean deviation around mean

We know, Sum of deviation of variate from their A.M. is always zero that is $\sum(x_i- \mu)$ where $x_i$ are all the elements and $\mu$ is the arithmetic mean. Also mean deviation is the mean of the ...
user avatar
0 votes
1 answer
36 views

Standardising third moment

I am assigning values to objects in a process. I would like the values to end up being normally distributed with variance one. For this I standardise them by subtracting their average from each and ...
user avatar
0 votes
0 answers
25 views

Test statistic of sample mean of non identical Gaussians

It is well known that given iid gaussians $Y_i \sim \mathcal{N}(m, v^2)$, with unknown mean and variance, then $t = \frac{\hat{m}-m}{\hat{v}/\sqrt{n}}$ follows a student-t distribution with $n-1$ ...
user avatar
1 vote
0 answers
22 views

Is there any mathematical relation between a harmonic mean and the harmonic mean of shifted values?

Let $H$ be the harmonic mean of a set of reals $x_i$. Can we say anything about the harmonic mean $H'$ of the same set of values, but for which each value is increased by a constant $c\,$? That is, $$...
user avatar
1 vote
1 answer
103 views

Expected value of cross tabulation / contigency table [closed]

I’ve got a pretty interesting problem and I can’t figure out how to address it. I can’t even find a similar problem on the internet. I have a cross tabulation / contigency table like this: 72251100 ...
user avatar
0 votes
0 answers
13 views

Coupling between mean and standard-deviation

For a one-sided distribution such as Poisson or the exponential distribution (but not specifically those particular one-sided distributions), $$ p_x(\alpha) = 0 \qquad \forall \alpha<0 $$ is there ...
user avatar

1
2 3 4 5
28