What is Estimation: Definition and 205 Discussions

Estimation (or estimating) is the process of finding an estimate, or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is derived from the best information available. Typically, estimation involves "using the value of a statistic derived from a sample to estimate the value of a corresponding population parameter". The sample provides information that can be projected, through various formal or informal processes, to determine a range most likely to describe the missing information. An estimate that turns out to be incorrect will be an overestimate if the estimate exceeded the actual result, and an underestimate if the estimate fell short of the actual result.

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  1. G

    Drag Estimation for a Subsonic Aircraft

    Homework Statement The small scale drawing given in the Annexure shows the general arrangement and dimensional data on an early version of the English Electric “Canberra” B.1 bomber, powered by two Rolls Royce “Avon” jet engines. It was and is an extremely successful aircraft, designed by W E...
  2. S

    Accurate estimation of complex eigenvalues

    Hello, I use Arnoldi iterative algorithm in order to compute the eigenvalues of a matrix. I know that the eigenvalues are of the form \lambda(1+j/c) and I can totally estimate them. The problem that occurs is that both the range of \lambda_0 and c is for example [100,1000]. That means that there...
  3. B

    Can Saggital Motion Help Estimate Frontal Displacement in Treadmill Walking?

    Hello everybody, I hope I am posting this under right topic. I am running a research project and we are recording videos of subjects from both frontal (back) and saggital (side) plane while they are walking on the treadmill. I put 10cm long calibration marker on the back of the subject. This...
  4. O

    Efficient parameter estimation of marginal distribution

    hi all, the situation is this: i have a conditional PDF f_{X|(D,S)}(x|d,s) and the unconditional PDFs D and S, f_{D}, f_{S}. Now, I can marginalize the joint PDF f_{X,D,S}=f_{X|(D,S)}f_{D}f_{S} by integrating over d and s over their respective supports. What I'm really interested in is a...
  5. M

    Estimation Theory: Get Help Understanding Binomial Proportion

    I got a question on estimation theory. Can anyone explain it to me or give me a link with some tut and solutions so I can get a better understanding. I got a maths question which i have asked for help but no one has replied yet. Since it was a statistical question I should have posted it...
  6. P

    What is the best estimate for the unknown parameter in a normal distribution?

    Hello everyone, I just started reading "Fundamentals of Statistical Signal processing" by Steven Kay and just got done with the first chapter, which describes the estimation problem, PDFs etc. It has some very interesting problems at the end and some of them have me a bit confused. I think...
  7. K

    Conditional & uncoditional MSE (in MMSE estimation)

    Hi, 1- Please explain conditional & unconditional mean square error, and their difference. 2- Which one is the solution for minimum MSE estimation? (that is conditional expectation: E \left[ X|Y \right] . I meant which one is minimized by selecting the conditional expectation.) 3- What is...
  8. C

    Valid Estimation of Square Roots?

    I've been playing around with a forumlaic representation of a known square roots estimation method and I came up with this: This estimation has several interesting properties to it which I've been looking into. My main concern is the fact that I'm using SQRT(x) in the equation which...
  9. J

    Alternating series, error estimation & approximation

    Homework Statement \Sigma(-1)^{n+1}\frac{1}{n!} How many terms will suffice to get an approximation within 0.0005 of the actual sum? Find that approximation. Homework Equations No idea.The Attempt at a Solution What I tried doing is setting my absolute value of the series less than 0.005, but...
  10. B

    Compressed Hydrogen tank mass estimation

    Does anyone know how to calculate the mass of compressed hydrogen tank at certain pressure. The tank is cylindrical with hemispherical ends. I have pressure,radius,wall thickness and length,internal volume and density of the material. The tank is a Type IV tank.(Composite tank with...
  11. 3

    Error Estimation for Simpsons Method

    Homework Statement Find the error estimation for the integral \int(1+x^2)^\frac{1}{4} with limits [0, 2] for n=8. Homework Equations \epsilon\leq \frac{|f^{(4)}_{max}(x)|(b-a)^5}{180n^4} The Attempt at a Solution The tricky part about this problem is finding f^{(4)}_{max}(x)...
  12. T

    Estimating Total Air Molecules in a Room | Help with Homework Statement

    Homework Statement Estimate to 1 significant figure the total # of air molecules in this room (l=20ft, w=14ft, H= 8ft) Find molecules/room Homework Equations 1 mole = 22.4 liters 6.02 x 10^23 molecules = 1 mole The Attempt at a Solution volume of room = 2240 ft^3 or approx 683...
  13. belliott4488

    Kernel density estimation for non-I.I.D. data

    I am wondering if Kernel Density Estimation (KDE) is appropriate for some data analysis I'm working on. I have a simulated process that produces a large number N of pieces of debris, and I want to know how these objects are distributed spatially. In other words, I'd like to estimate a density...
  14. M

    Solve Point Estimation Problems: 95% Confidence, 3% Error

    I have 2 problems I am currently stuck on.. one being In a large sample study according to a report by the U.S. surgeon general, electrical engineers have the lowest smoking rate among all workers surveyed. Only 16% of the male electrical engineers in the sample smoke cigarettes regularly. How...
  15. M

    Error Estimation for Refractive Index of Dielectric Material

    Homework Statement i did a lab on determination of refractive index of an opaque dielectric material, using the brewster angle. We took a couple of readings on a spectrometer at the position of complete extinction, now how do i get the error estimate ? The angles were taken to the nearest...
  16. E

    Estimating Distance from Earth to Sun Using Trigonometry

    Homework Statement The problem from the book states The problem I am having is actually trying to figure out how someone else's suggested solution. His idea was to take a value R for the mean radius of the sun: R=6.96x10^{5} km And use trig to find out a rough distance. Homework...
  17. E

    Statistics: Method of Moments/Maximum Likelihood Estimation

    Homework Statement f(x;theta)=Exp(-x+theta) Find parameter estimates for variable 'theta' using maximum likelihood Estimator and Method of Moments. Homework Equations Log(x; theta) = Log(Exp(-x + theta)) -- For MLE Integral from theta to infinity of (x*Exp(-x + theta)) = xbar -- For Method of...
  18. M

    How Can I Estimate Heat Transfer in a Rotating Cylinder with Flow on Both Sides?

    This should be a fairly easy problem, although my Heat Transfer is quite rusty. I'm trying to get a ballpark estimate for a rotating cylinder that has flow on both the inside and outside. I know the temperature of the air at the inlet and outlet and am trying to get a decent estimation for...
  19. G

    Puzzles Estimation using extreme values

    Homework Statement Estimate the length of the Sydney Harbour Bridge that lies between the pylons. Give your answer in metres and give a justification for your answer. Homework Equations No equations needed I guess. To answer this type of question you need to consider extreme values and...
  20. S

    What is the Confidence Interval Formula for Maximum Likelihood Estimation?

    L(x_1,x_2,...,x_n;\theta)=\Pi _{i=1}^n (\frac{\theta}{2})^x (1-\frac{\theta}{2})^{1-x} = (\frac{\theta}{2})^{\Sigma^n_{i=1}x_i}(1-frac{\theta}{2})^{n-\Sigma^n_{i=1}x_i} Correct so far if f(x) = (\frac{\theta}{2})^x (1-\frac{\theta}{2})^{1-x} ? lnL(x_1,x_2,...,x_n;\theta) =...
  21. N

    Maximum Error in Taylor Polynomial for cos(x) on Interval [-.25, .25]

    Homework Statement Find the maximum error in approximating cos(x) by its Taylor polynomial of order 2 on the interval [ −.25, .25]. Justify your answer using the Remainder Estimation Theorem. Homework Equations |R3(x)<=M/3! |x|^3 The Attempt at a Solution |R3(x)<=M/3! |x|^3...
  22. J

    Signal processing + parameter estimation

    Is parameter estimation in DSP concerned with things such as bit error rates, maximum likelihood detection etc ... ? If not, can someone point me in the right direction so I can find some learning material. thanks
  23. N

    Crude geometric estimation or am I missing something?

    Homework Statement I'm doing a report for a physics lab experiment where we are calculating the radius of the Earth by measuring the time it takes to see the sunset from the base of a cliff looking out into the pacific ocean till when it sets in relation to an observer at the top of the...
  24. A

    Linear Gaussian parameter estimation

    Hi, I have a multivariate linear-gaussian model and I am trying to estaimte a particular scalar set of parameters of the model. I know how to derive the MLE in order to find the matrices A and Q (linear transfer function and covariance respectively). I take the log of the joint...
  25. J

    Solar Dryer Drying Time Estimation

    Homework Statement The problem is fairly simple (hah): estimate the time it will take for a solar dryer (which I have to design) to dry 50 pounds of fruit from 80% water to 10% water. Homework Equations It seems there are at least a few equations that give an approximation for...
  26. T

    Estimation of parameters using maximum likelihood method

    Homework Statement Let's have random value X defined by its density function: f(x; \beta) = \beta^2x \mbox{e}^{-\beta x} where \beta > 0 for x > 0 and f(x) = 0 otherwise. Expected value of X is EX = \frac{2}{\beta} and variance is \mbox{var } X = \frac{2}{\beta^2}. Next...
  27. K

    Estimation of Work in Gas Compression - Thermodynamic

    What kind of thermodynamic process is the compression of a gas when the volume varies reducing it, and the temperature increase, and there is an exchange of temperature with the exterior (the walls of the compressor are refrigerated, but I assume that the gas will increase its temperature a...
  28. D

    Least-squares estimation of linear regression coefficients

    AFAIK, there are two basic type of linear regression: y=ax+b and y=a2 + bx + c But I have to do the same with the function y = asin(x)+bcos(x). Here is what I have done: We have: \begin{array}{l} \frac{{\partial L}}{{\partial a}} = 0 \frac{{\partial L}}{{\partial b}} = 0Continue...
  29. C

    Integral arising in estimation of discrete series

    I'm trying to solve f(t;a,b)=\int_a^b\sqrt{t-x^3}dx or find a good estimate for it. The problem is 'nice', and so various niceness assumptions apply: 0\le a\le b\le t -- and if other assumptions are needed, they probably hold. :D An example of a bad estimate would be (b-a)\sqrt{t-a^3} --...
  30. M

    Infinite series estimation using integral test

    Homework Statement Estimate \sum^{\infty}_{n=1}n^{-3/2} to within 0.01 Homework Equations \int^{\infty}_{n+1}f(x)dx\leq R_{n} \leq \int^{\infty}_{n}f(x)dx The Attempt at a Solution So my strategy was using the above formula to find Rn, where Rn = 0.01 or 1/10^2. Then that will give me the...
  31. H

    Astronomy Olympiad Estimation Question

    Homework Statement Q. Given that the population of Mumbai is about 13,000,000. Estimate the amount of tea that would be consumed by the city in a day? 2. The attempt at a solution Now at first place I could not understand why such kind of a question is given in Astronomy Olympiad...
  32. R

    Help with choosing method for duration estimation

    Hello everybody, I am new here and I am not sure whether I put this question in a correct forum. If not I am sorry...anyway I hope you help me... ***** Before all: ***** TESTED: SSD METHOD DOES NOT WORK HERE SUFFICIENTLY RELIABLY. Here it is: ***** Description: ***** Imagine we...
  33. M

    Gamma and Weibull location parameter estimation

    Hi all, I have a set of samples and I would like to detect the probability distribution that best represents the data. I'm using the kolmogorov-Smirnov test to verify the goodness-of-fit for some well-known distributions, like Gamma, exponential and Weibull. Since I don't know the...
  34. L

    Lifting line theory numeric estimation

    hi, i am in the final yr aerospace engg...i am trying to write a program on MATLAB to calculate the lift distribution over a wing using the numerical estimation based on the classic(prandtl) lifting line theory...however, due to my relatively limited exposure to MATLAB i am having trouble...
  35. J

    Can You Estimate Parameters for a Non-Closed Form Probability Distribution?

    I have a probability distribution of the form \sum_{i=0}^n f(n,x,y). There is no closed form expression for it. I need to know if there is any method that I can use to estimate the parameters {n, x, y} given some data from the above distribution. I've tried a maximum likelihood approach, but...
  36. A

    Hint for Quantum Computing Question Regarding QFT's and Eigenvalue Estimation

    Homework Statement I've pasted the actual question below: http://www.zeta-psi.com/aj/qip5b.png I don't think there are many quantum computing specific things here other than the circuit (which I can derive easily if I can figure out the algorithm) Homework Equations The Quantum Fourier...
  37. N

    Covariogram estimation for the process contaminated with linear trend

    Let {S(t), t=1,2,...} be a zero-mean, unit variance, second-order stationary process in R^1, and define Y(t)=S(t)+k(t-(n+1)/2), t=1,2,...,n. Then the process Y(t) is not second-order stationary process since it is contaminated with linear trend, k – degree of contamination. Define R(h)...
  38. N

    Covariogram estimation for the process contaminated with linear trend

    Let {S(t), t=1,2,...} be a zero-mean, unit variance, second-order stationary process in R^1, and define Y(t)=S(t)+k(t-(n+1)/2), t=1,2,...,n. Then the process Y(t) is not second-order stationary process since it is contaminated with linear trend, k – degree of contamination. Define R(h)...
  39. R

    Remainder Estimation Theorem & Maclaurin Polynomials :[

    Homework Statement Use the Remainder Estimation Theorem to find an interval containing x=0 over which f(x) can be approximated by p(x) to three decimal-place accuracy throughout the interval. Check your answer by graphing |f(x) - p(x)| over the interval you obtained. f(x)= sinx p(x)=...
  40. R

    Very interesting estimation problem

    "Annie and Evelyn observe that, on average, it takes approximately 10 days for a small glass of water to completely evaporate when left outdoors. What would they estimate for the average annual precipitation on Earth?" (Answer in depth of precipitation) Here's my though process but I have a...
  41. C

    Help on estimation the gradient of a sigal sequence

    Dear All, I have a signal, which is a time series from measuring some quantity. The trend of the signal is decreasing. However, due to noise, the signal is fluctuating. Is there some method to get a good estimation of the gradient of the signal, i.e. the average reduction of the quantity...
  42. E

    Point Estimation Question

    Suppose I have a total population with x/y percent having a certain property q. If I take an n-number sample of this population, what is the most likely number of elements in this sample that will have property q? I want to say the fraction z/n will be as close to x/y as possible where z is...
  43. Gamma

    Learning Rounding & Estimation with Front End Math

    I am new to this type of math. I need help.... Can anyone point to me to a good website where I can learn about rounding and stuff. Here is another one I am struggling with. I looked in the internet could not find one that really explains it well How to estimated 3.9 * 7.4 using...
  44. K

    Uncertainty without a given estimation

    This is regarding a problem on approximate uncertainty. How do you just calculate an approxiate uncertainty of a circle when a radius is given?
  45. D

    Heat Transfer Rate & Estimation in Air-Steam Flow System

    Thought this would be the most appropriate forum to ask for help Air flows through a copper inside tube and is heated by saturated steam condensing on the outside of the tube. 1. Determine the rate of heat transfer to the air at 3 different flow rates of the air (rotameter readings 10, 20...
  46. S

    Fermi Style Estimation Question

    Have been set a rather tricky question in physics, and wondered if you had any ideas on how I would go about answering it... It is based on Fermi style estimation to try and encourage one to estimate and guess, the question is... 'How many particles of ionising radiation pass through your head...
  47. C

    Exploring Galaxy Surveys: Shot Noise Estimation

    I am reading about galaxy surveys. I want to know what is shot noise ? how we estimate it into real and Fourier space ? I am basically reading astro-ph/0503603 & astro-ph/0503604. I am not able to solve exercise 4, 5, 6. I will be thankful, if anybody can provide me some reference.
  48. K

    How Accurate is the Freezing Point Calculation for Ethanol at 1000 atm?

    ethanol 46g/mol freezes at 3.65degC density changes from 0.789g/cm-3 to 0.801g/cm-3 latent hear of fusion 8.68kJ/mol. freezing point at 1000 atm. i calculated the ansfer from an example and just want to verify if its correct. dp/dt=(dfusH)/(t*dfusV) rearanged to dt=(dp*t*dfusV)/dfusH...
  49. C

    How can I estimate the fatigue life of a component subjected to a rotating cam?

    I am working on a physics problem in a project to estimate fatigue life of a component. There is a cam rotating with an offset of 10mm rotating at an rpm of 230. The component is a cantilever fixed at one end is getting hit by this cam while it is rotating. The cam is at the other end of...
  50. J

    Volumetric estimation of iron(II)ions

    Hi ppl, I have an electrochemisry question. Explain why dilute sulphuric acid, rather than dilute hydrochloric acid, is used as a source of hydrogen ions in the volumetric estimation of iron (II) ions with potassium manganate (VII).
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