For questions about estimation and how and when to estimate correctly
Questions tagged [estimation]
1748 questions
4
votes
2 answers
Definition of accuracy to three decimal places.
Let us say that we have estimated the value of some constant $S$ as a number $T$ with $|S-T|<0.001$. Does this mean that the number $T$ is correct to $3$ decimal places? My textbook seems to indicate so.
My concern is that the numbers at the first…
The Cryptic Cat
- 1,417
4
votes
4 answers
Logically deducing what's larger $0.8^{10}$ or $0.81^9$?
Edit: I initially wrote the question backwards
I got a question recently, what's larger $0.8^9$ or $0.81^{10}$, don't have to calculate the exact number obviously, just figuring out which is larger. I'm not really sure how to proceed logically. I…
user3002540
- 159
4
votes
1 answer
Cramer-Rao lower bound for any unbiased estimator
The first part of a question I am trying to solve asked to find the maximum likelihood estimator for $\theta$ for a pdf $f_X(x)=\frac{2x}{\theta^2}$, $0 < x \le \theta$ , $0$ otherwise. ($X_1, X_2, X_3, \ldots , X_n$ are independent and iid)
What…
samp1920
- 139
4
votes
0 answers
Maximum likelihood estimator(MLE)
Consider a sample from a distribution with PDF
$$f(x) = \begin{cases} \frac{1}{2}(1+\theta x), & -1 \leq x \leq 1\\
0, & otherwise \end{cases} $$
find the maximum likelihood estimator of $\theta $.
I know that
$$ L(p) = f(x_{1},\theta) .…
cecemelly
- 195
2
votes
1 answer
show that the sample median of normal distribution is median unbiased
$X_i \sim N(\mu,\sigma^2)$, $i = 1,2,\ldots,n$.
Show that the sample median is unbiased in median for $\mu$.
I have obtained the pdf of sample median for $n=2m+1$ as:
$$f(x_{(m+1)}) = \frac {(2m+1)!} {m!m!} \Phi\left( \frac{x-\mu}{\sigma} \right)…
kris91
- 401
2
votes
2 answers
What's the best strategy to count the eggs in the jar?
It's Easter time, and in my workplace we have a "Count the eggs in the jar!" kind of game.
What would be the best mathematical strategy to get as close as possible to the correct count?
Update: The contest has ended, the number of eggs is (Hover…
Adi
- 139
2
votes
1 answer
sine function description using three points
Is there any way to find the parameters of a sine wave ($A$, $w$, and $ \phi $ for $A \sin(wt+\phi)$ ) using just three points (samples)?
Thank you in advance for your help.
Mohsen
- 23
2
votes
1 answer
Some help with calculating the time remaining please???
I am a solid technology troubleshooter and problem solver, but when it comes to numbers.....well I suck at it. :/
I am trying to calculate how much time a program will theoretically finish copying the data from a malfunctioning hard drive so I can…
Braden's PC's
- 121
2
votes
3 answers
Estimating a powered decimal
A friend told me his colleague estimated 0.95^32 using nothing, just approximating it in her head to be about 0.2.
My calculator gives the answer 0.1937114844585.
How would one go about doing something like that?
I've been burried in contemplation…
user464553
- 21
- 1
2
votes
1 answer
finding maximum likelihood estimate from dependent binomial rvs
let $X_{1}$, $X_{2}$, $X_3$, $X_{4}$ be iid bernoulli rvs with $\mathbb{P}(0)=0.5$, $\mathbb{P}(1)=0.5$.
$Y_{1} = X_{1}+X_{2}+X_{3}$ and $Y_{2}=X_{1}+X_{2}+X_{4}$
$Y_{1}$, $Y_{2}$ are dependent binomial rvs by definition.
I need to find max…
xplore29
- 55
1
vote
1 answer
Statistics question: Estimating mean when standard deviation is known
I am reading a textbook to learn more about statistics. This section is about estimating the mean of a population when standard deviation of the population is known.
My simple question is this: How can we know the standard deviation of a population…
soroor
- 11
1
vote
0 answers
Derive Maximum Likelihood Estimator of a Generalised Linear Regression Model
I understand how to find the MLE estimator for $b$ if it is a simple linear regression model. However, when $u\sim N(0,\sigma^2\Omega)$ where $\Omega\ne I$. I am getting confused. The model is: $Y=Xb+u$
How does this differ? I am aiming for…
hseager
- 13
1
vote
1 answer
How to calculate the initial approximation in Newton - Raphson division algorithm.
I would like to know how to calculate first approximation in N-R division algorithm. I want to find the inverse of R. Here is the formula:
$x_{i+1} = x_{i}(2-R*x_{i})$
I'm trying to implement it in my program, so I need some algorithm to calculate…
user3448282
- 113
1
vote
0 answers
Find a weakly singular kernel function for an estimation of a kernel
Let $\Omega\subset\mathbb{R}^n (n>1)$ be a bounded domain and $0<\alpha
user34632
1
vote
0 answers
Non-sequential German Tank Problem
I have a bag containing $n$ coins. Each coin has a unique integer on it in the range $[1, m]$. As a corollary, $n \le m$.
We may sample $k$ coins without replacement where $k < n$. Given that we have knowledge of the numbers on $k$ coins but we…
NeRoboto
- 203