For questions about estimation and how and when to estimate correctly
Questions tagged [estimation]
1748 questions
1
vote
2 answers
How to calculate this ratio for use in pro-rata forecasting
This is really a very simple question, it's more the understanding I need rather than a simple answer.
If I have two arrays, A with 10 elements (A1, A2, ...), and another, B, with 5 elements (B1, B2, ...) and I want to base the missing 5 elements on…
Rapid
- 171
1
vote
1 answer
Bias of proportion estimator
The typical estimator for a population proportion $p$ is the sample
proportion ${\hat p_1} = {X \over n}$, where $X$ is the number of
successes in a random sample of size $n$. However, in the case when
the population proportion $p$ is small…
Pedro Alonso
- 399
1
vote
1 answer
MAP estimator of Z=X/Y estimating X
The probabilities are given
$$pdf(y)=\lambda_ye^{-\lambda_y y}, y\geq0$$
$$pdf(x)=\lambda_xe^{-\lambda_x x}, x\geq0$$
I have the observation such that $z=x/y$. I want to estimate $x$. First, I found
$$pdf(z)={\lambda_x\lambda_y\over{(\lambda_x…
Don
- 636
1
vote
0 answers
Consistent estimator for $\mathbb{E}[\mathbb{E}[f(X_1,X_2)|X_1]^2]$
Suppose $(x_{i})_{i=1}^n$ are i.i.d. sample. I want to construct a consistent estimator of $\mu=\mathbb{E}[\mathbb{E}[f(X_1,X_2)|X_1]^2]$, where $f(x_1,x_2)\ne f(x_2,x_1)$. I use $X_1$ for random, $x_1$ for realization.
My attempt: $\hat{\mu} =…
user1292919
- 1,895
1
vote
0 answers
constrained non linear estimation degrees of freedom
I would like to know how many degrees of freedom are in this model, and whether it the following makes sense. I have a set of parameters ($\theta_i$) that I constrain to have a mean of one ($\bar\theta_i = 1$ & $\theta_i > 0$). I impose this…
Cyrillm_44
- 111
1
vote
2 answers
successive approximation for sine, using pencil and paper
I'm looking for a relatively simple algorithm that can quickly be done by hand to refine an initial estimate for the sine of an angle in degrees.
I've memorized a few landmark values for sine and come up with some simple techniques such that I can…
brianmearns
- 837
1
vote
0 answers
How to improve a poisson based estimator using variance reduction techniques
Given a random number $X \sim Pois(\mu)$ for some random, i.i.d $\mu$, I'm trying to estimate $P(X \ge x)$ by simulation. The approach is to use a raw/classic estimator, where I generate a bunch of $X$, by first generating an equally large number of…
Clearer
- 218
1
vote
1 answer
Estimation Question - London Eye
Good afternoon, I was recently at an assessment center and was asked an estimation question. This was the first one I've ever done so was wondering how everybody else would go about solving the problem.
I had 10 seconds to look at the attached…
Obsi
- 13
1
vote
1 answer
Behaviour of $\sum_{k=1}^n\left(\left(\frac{3}{2}\right)^k\ (\mathrm{mod}\ 1)\right)$
Using Mathematica I found that the relation
$$\sum_{k=1}^n\left(\left(\frac{3}{2}\right)^k\ (\mathrm{mod}\ 1)\right)\approx\frac{n}{2}$$
seems to hold. Actually, every fraction of the form $\frac{b}{a}$, with $b>a$ and $\mathrm{gcd}(a,b)=1$, seems…
Carolus
- 3,279
1
vote
2 answers
Significant figures addition/subtraction rounding?
I thought you round to the same place as the number with the addend with the least precision. For example, if you had $25.63+ 42.3$ the answer would be rounded to the tens place ($67.9$).
However, my chemistry teacher just said that it would be…
Jonathan Lam
- 803
1
vote
1 answer
Sufficient statistics problem
$X_1, X_2, \ldots, X_n$ are iid $N(0,\theta), 0 < \theta < \infty$
Show $$\sum_{i=1}^{n} X_i^2$$
is a sufficient statistic for $\theta$.
My attempt at this is
$S = (X_1^2 + X_2^2+\cdots+X_n^2)/n$
$$E[S]= \frac{1}{n}…
samp1920
- 139
1
vote
1 answer
How many bathtubs in a min?
During the summer about $750,000$ gallons of water fall over the edge of Niagara Falls every second. If an Olympic sized swimming pool holds about $660,000$ gallons of water, how many Olympic sized swimming pools could the water that flows over the…
Rock
- 13
1
vote
1 answer
Likelihood and maximum likelihood
what is the likelihood, log-likelihood and MLE of;
$$θ(θ+1)x^{θ−1}(1−x)$$
any help greatly appreciated
Anthony West
- 11
0
votes
1 answer
Estimating the Growth Rate of Worms
I would like to know how much worms I'd have on hand given an initial amount and period of time. Here are some metrics regarding the growth rate of these worms.
2.45 - 3.5 cocoons per adult worm per day.
2.5 - 3.8 worms per cocoon
Incubation…
rtheunissen
- 103
0
votes
2 answers
Estimating arctan to below
How can I estimating
$$
\arctan(\lVert x-y\rVert),
$$
to below (where $(x,y)\in\Omega\times\Omega, x\neq y$, $\Omega\subset\mathbb{R}^n, n>1$ bounded domain)?
Can you give me a hint please?
Someone said me to use
$$
\lvert x\rvert\ll 1\Rightarrow…
mathfemi
- 2,631