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. O

    A Measurement and error (error estimation and propagation)

    Description of the situation I have measured the incident number of electrons in a channel electron multiplier at different light polarization angles (a photoelectron angular distribution measurement). The events follow a poisson distribution and as far as I know the number of electron counts in...
  2. jlmccart03

    Alternating Series Estimation Theorem

    Homework Statement Using the power series for ln(x + 1) and the Estimation Theorem for the Alternating Series, we conclude that the least number of terms in the series needed to approximate ln 2 with error < 3/1000 is: (i) 333 (ii) 534 (iii) 100 (iv) 9 (v) 201 Homework Equations ln(x+1) =...
  3. quantumdude

    A Estimation of Hurst Exponent Using Rescaled Range

    Hey folks, long time no see! :woot: I am trying to estimate the Hurst Exponent for financial data using the R/σ (Rescaled Range) method. I have no authoritative source for this method. All I have are web pages (and we know how accurate those are). Specifically, I've been using the following...
  4. N

    How to calculate Time Delay Estimation?

    I have 2 data files, which links are attached below: Transmitted data https://www.dropbox.com/s/0nmhw6mpgh7upmv/TX.dat?dl=0 Received data https://www.dropbox.com/s/xgyo6le3bcmd25r/RX.dat?dl=0 Those binary data are read by this MATLAB code: %% initial values: nsamps = inf; nstart = 0; %% input...
  5. N

    Understanding time delay estimation for GPS?

    I really need help to understand these questions which is highlight, for the GPS situation, I hope anyone who has been working in this situation before, please help me to have a clear understanding about "time delay estimation": Here is the scenario: 1. Suppose I know precisely I have transmit...
  6. A

    A Orbit Estimation: Range & Doppler Measurements for Position & Velocity

    Suppose I have to determine position and velocity of spacecraft from Range and Doppler measurements. Does range measurement only give position estimate and doppler only velocity estimate? Or range can give both position and velocity?How are they related?
  7. S

    Estimation of material loss through electrical resistivity

    Hi all, I'm doing a little project about the wear of materials for tools for cutting machines.Yesterday, I was reading wikipedia page about electrical resistivity and I thought if it might be possible to evaluate the estimate the material loss of the tool through the measure of electrical...
  8. B

    I Robust linear estimation to guess parameters

    Hi guys! I am working on a project and I need to perform a robust linear estimation as described here: https://postimg.org/image/t9b9fybtt/ I have to do this to the equation 43: https://postimg.org/image/x4eniiuzl/ I have assumed that the final function that I have to minimize, basing on both...
  9. B

    I How can robust linear estimation be carried out in a non-linear context?

    Hi and thanks to everyone for his/her attention. I have to minimize a function that depends on several parameters. The aim of minimizing that function is to actually guess these parameters, which are unknown. The thing is that the author of the pdf from which I have to make the calculations...
  10. J

    I Problem with this estimation lemma example

    I have been trying to show that $$\lim_{U\rightarrow\infty}\int_C \frac{ze^{ikz}}{z^2+a^2}dz = 0 $$ Where $$R>2a$$ and $$k>0$$ And C is the curve, defined by $$C = {x+iU | -R\le x\le R}$$ I have tried by using the fact that $$|\int_C \frac{ze^{ikz}}{z^2+a^2}dz| \le\int_C...
  11. H

    Iron loss curve estimation

    Hi all, I am recently calculating the iron loss in a permanent magnet synchronous machine with a speed of 24000 rpm (electrical frequency 800 Hz). However, the iron loss data from the data sheet is not sufficient since only frequency of 50 Hz, 100 Hz, 200 Hz, 400 Hz, 1000 Hz and 2500 Hz are...
  12. R

    MHB [Cognitive Robotics] state estimation

    Hey guys, I need some help. Here's my task: Here's what I came up with: I need to calculate prob(x1|z1), prob(x1|z2) and so on and then just write down which has the highest probability. To do that, I would use Bayes rule, but for that, I need p(z1|x1) and p(z1). How do I get these? I have...
  13. J

    Elementary questions about error estimation

    Homework Statement We measure the temperature with a thermometer and we get these results: 3.3 +- 0.1 ºC 3.5 +- 0.1 ºC 3.6 +- 0.1 ºC What is the temperature? Homework Equations Average = Sum of values/amount of measurementes The Attempt at a Solution Well, I calculate the average and I...
  14. wrobel

    A Can Estimation of a Function Determine Exponential Decay for Vector-Functions?

    Let ##x(t)\in C^1(\mathbb{R}_+,\mathbb{R}^m)## be a vector-function such that 1) ##\|x(t)\|+\|\dot x(t)\|\to 0## as ##t\to\infty## and 2) for all ##t>0## one has ##\|x(t)\|\le c_1\|\dot x(t)\|##Is it true that ##\|x(t)\|\le c_2 e^{-c_3t}##? Here ##c_i## are positive constants.
  15. I

    I Semi ln plot- uncertainty estimation

    Hello there! There is a problem with calculating the uncertainty from semi- ln plot. The linear fitting gives standard errors as you can see in attached picture. In the Y axis are ln J values, obviously. If the intersection with y-axis, x=0, then we get the point y=b=-33,21, and it's ln J', so...
  16. A

    How Can I Increase My Lawn Sprinkler System's Flow Rate?

    I have a DIY project for a lawn sprinkler system but my flow rate is insufficient : if my setup is to work properly, the sprinkler manufacturer suggests a flow rate of 2880 litres per hour at a pressure no less than 2 psi. I measured the flow rate of my current garden faucet, which is connected...
  17. R

    Secant Method Minimum Estimation

    Homework Statement I am having some trouble understanding the following solved problem: Use two iterations of the Secant method to estimate where ##x^2 -x## has a local minimum. Start with ##x^{(0)} =1##, ##x^{(1)} =1/2.## Answer: Homework Equations Secant iteration: $$x_k = x_{k-1} -...
  18. B

    I How to Estimate Uncertainty for a Physical Quantity with Dependent Variables?

    I have a physical quantity A defined as ##A=(74.5 B^2*(M+N))^{1/3}## where B, M, N and relative uncertainties are given. And M and N are dependent on B. Could you show me how to calculate and estimation for the uncertainty on A? Thanks a lot
  19. M

    Estimation - Student-t distribution - Confidence Level

    Homework Statement [/B] A company produces batches of 1800 axle shafts . These are tested to determine the proportion of those with too rough surface according to the standards set in the industry. The quality control department of a sample of 150 axle shafts in a lot and concluded that there...
  20. W

    Bayesian estimation via MCMC

    Hi folks. I have the following question.I have a model M containing 20 adjustable parameters k = {k_j}. I also have 40-50 measured temporal profiles e = {e_i} at my disposal. I can use M to predict the experimental values after solving complex systems of differential equations.Consequently, I...
  21. W

    MHB Bayesian parameter estimation via MCMC?

    Hi folks. I have the following question. I have a model M containing 20 adjustable parameters k = {k_j}. I also have 40-50 measured temporal profiles e = {e_i} at my disposal. I can use M to predict the experimental values after solving complex systems of differential...
  22. Alettix

    Estimation of data stored on a CD

    Hello! I would be very happy if you could lend me a helping hand with the following problem. :) 1. Homework Statement We know that a CD is read with a laser with a wavelenght of λ = 1 μm. a) Estimate the data stored on the CD. b) We know that the CD contains 80 minutes of sound. How fast is it...
  23. B

    How to Find Least Square Estimates for Object Weights with Normal Error?

    Homework Statement Suppose that object 1 weighs \theta_1 and object two weights \theta_2. Then each object is weighed once and then together getting three observations y_1,y_2,y_3. The scale gives unbiased weights with normally distributed error (constant variance) Find the least square...
  24. R

    Correcting a mass estimation under acceleration

    Hi, I have seed of a project forming but need some help with some physics in it : What I'm trying to do : I need to weigh a sample using a load cell, so far so good, but the load cell is on a moving platform, a ship. I think I know that if the object being weighed and the load cell were moving...
  25. moenste

    Vertical movement: velocity / time graph, height estimation

    Homework Statement A ball is thrown vertically upwards and caught by the thrower on its return. Sketch a graph of velocity (taking the upward direction as positive) against time for he whole of its motion, neglecting air resistance. How, from such a graph, would you obtain an estimate of the...
  26. E

    Estimation example from Giancoli

    Hello, I´m a bit math-challenged and just started to brush up on both physics and mathematics simultaneously but I'm still at absolute beginner status and I don't want to go on in the book as long as I can't even figure out such a simple example. I'm using the Giancoli textbook on physics for...
  27. E

    Kernel Estimation: Questions about Bandwidths & R Functions

    Hi there! I'm new in the technique of Kernel Estimation, so it could be that the following questions are really elementary. There is something I don't understand about the bandwidths. Using R I have two functions to perform the estimate: kde2d from MASS bkde2D from KernelSmooth Here are my...
  28. P

    Can a Flywheel Store 1 MW of Power for 50 Seconds with Only 33% Energy Loss?

    Hi fellow scientists and engineers, I have a question regarding the design of a flywheel. I know that the actual engineering of a flywheel is very complex and in no way I should expect actual practical answers from this simple question. I'm just trying to get some estimates for a renewable...
  29. N

    MHB How Does Archimedes' Estimation of Pi Hold for n=4, 8, 16, 32, ...?

    It has been eons since I've done any trigonometry, but I just can't prove how this following relationship holds for $n = 4, 8, 16, 32, \dots$ The relation is: $$ 2 \biggl( \! \frac{A_{2n}}{n} \! \biggr)^2 = \, 1 - \Biggl( \sqrt{1 - \frac{2A_n^{\phantom{X}}}{n}} \, \Biggr)^{\!2} $$ I've subbed...
  30. R

    Speed Time Estimation from a video

    Homework Statement Watch the crash test video , and determine the following: 1. How fast is one of the crash test dummies thrown forward (the crash at :34 seconds) ? Pick either one, and be clear how you estimate this. 2. Assuming the speed you got from part (1), how high would a different...
  31. AngelLestat

    Thermal transfer estimation (to simulate a game)

    I am trying to get a formula to estimate the heat lose in an airship. Is a mod for KSP, things that have into account: pressure, wind speed, temperature, air viscosity, thermal capacity of the atmosphere, gravity, etc. There are things that can be ignored as shape (or just use constant...
  32. S

    How Does Fuel Consumption Scale with Speed in a Fiat Car?

    Homework Statement Five measurements of fuel consumption of a random Fiat car gives us data:v (km/h) l/100 km 70 --> 3.9+-0.1 90 --> 4.8+-0.1 120 --> 6.0+-0.1 150 --> 8.1+-0.1 160 --> 9.0+-0.1 We would like to check if for velocities greater than 70 km/h the...
  33. D

    Least Squares Estimation for two parameters

    Homework Statement Hi guys, so the problem is as follows: A set of n independent measurements y_{i}, i=1...n are treated as Gaussian, each with standard deviations \sigma_{i}. Each measurement corresponds to a value of a control variable x_{i}. The expectation value of y is given by...
  34. T

    Heat Transfer question, estimation of coefficients

    Hi, I've recently been given a series of questions on heat transfer to do and have done most of them with general ease, but this one question I've been stuck on for ages and i can't seem to figure out: "A double pipe heat exchanger is made up from a length of 25mm i.d. steel pipe of 2.5mm...
  35. Schnurmann

    Least Squares Estimation - Problem with Symbols

    Hi folks, 1. Homework Statement I don't fully understand the question statement, how is it supposed to be read? Question: Give a formula for the minimizer x* (to be read as x-star) of the function ƒ:ℝn → ℝ, x → ƒ(x) = ||Ax-b||22, where A∈ℝm×n and b∈ℝm are given. You can assume that A has rank...
  36. V

    What is the Best Way to Determine Sampling Accuracy in Large Populations?

    Good afternoon! Suppose I have a box with N marbles of different color and I want to know the ratio of the number of green ones to N (number X). The number of marbles (N) is so huge that there`s absolutely no way to get them all out of the box and count. What I do instead is I take a sample of...
  37. P

    Spherical Aberration Estimation

    Homework Statement Estimate the size of the spherical abberation of a spherical mirror of 1m-diameter and a focal length of 2 meter. (Hint: Calculate the size of the smeared image of a star at the focal point and compare it to the size (in arc-sec) of an extended object)Homework Equations The...
  38. R

    Seeking opinion of others on quantum systems control and estimation theory

    I am an EE graduate stumbled upon this exciting new field of research fusing control and estimation theory(EE) and quantum mechanics(Physics). I seeking opinion of experts and professionals regarding this field.I think it would be critical for development of new future quantum technologies and...
  39. A

    Using Newton Raphson for Root Finding and Parameters' Estimation

    Goood Day, I have a cubic root equation. I use Newton-raphson for finding the roots. I want to do parameter estimation (tuning of the equation parameters to be able to give better prediction) using experiment data. Can anyone help me on how to do this? Thanks for your anticipated help...
  40. B

    Error estimation using differentials

    Homework Statement A force of 500N is measured with a possible error of 1N. Its component in a direction 60° away from its line of action is required, where the angle is subject to an error of 0.5°. What (approximately) is the largest possible error in the component? Homework Equations...
  41. NTW

    Lift-dependent drag estimation

    I'm no engineer, but just a pilot trying to estimate the drag of my small two-place airplane from the relevant formulae. My plane is quite draggy, and from comparison with other aircraft data, I have taken Cd,0 as 0.043. Apart from this, I calculate the induced drag at a given speed from the...
  42. F

    Alternating Series estimation theorem vs taylor remainder

    Homework Statement Let Tn(x) be the degree n polynomial of the function sin x at a=0. Suppose you approx f(x) by Tn(x) if abs(x)<=1, how many terms are need (what is n) to obtain an error less than 1/120 Homework Equations Rn(x)=M(x-a)^(n+1)/(n+1)! sin(x)=sum from 0 to ∞ of...
  43. R

    Piping pressure head estimation

    Say there's a pipe that pumps a liquid that empties into an elevated tank The discharge end of the pipe is 5 m higher up than the suction but it goes over an intermediate obstacle, say, 20 m higher than suction level. Is the pump head requirement 5m or 20m? I'm confused. My gut feeling...
  44. W

    ML-inequality, Estimation of Line Integrals

    Problem: Let ##\vec{F}## be a vector function defined on a curve C. Let ##|\vec{F}|## be bounded, say, ##|\vec{F}| ≤ M## on C, where ##M## is some positive number. Show that ##|\int\limits_C\ \vec{F} \cdot d\vec{r}| ≤ ML ## (L=Length of C).Attempt at a Solution: I honestly have no idea where...
  45. P

    Crude estimation of a magnetic quadrupole

    Hi, Homework Statement I ran an experiment to determine Br(r), where Br was the radial magnetic field produced by a magnetic dipole. Having found the magnetic moment of the dipole, I would now like to determine the contribution to the magnetic field of the next order in the expansion (viz. the...
  46. Rorshach

    Normalization of wave function and estimation of values

    Homework Statement Hello, I have this problem with seemingly simple process, but there are things I either don't know, or make some stupid mistake on the way over and over. Here's the problem: At a particular time given by the wave function ψ(x)=N*x*exp(-(x/a)2) Determine N so that the wave...
  47. 2

    Estimation of the volume of a solid.

    Homework Statement Estimate the volume of the solid whose base is bounded by the graphs of y = x + 3 and y = x2 − 3, and bounded by the surface z=x2+y from above, using the indicated rectangular cross sections taken perpendicular to the x-axis (figure is not the actual graph of the functions...
  48. V

    Parameter Estimation, Non Linear Least Squares, Newton-Raphson

    Hello, Homework Statement I want to estimate a set of parameters by trying to minimize the sum of squares wrt to the parameter set given a simulation of a markov process and real data in Matlab. I have already implemented the Levenberg-Marquart (LM) Algorithm and it is converging to certain...
  49. S

    Torque estimation of an AC compressor

    Hi all, I'm planning to drive the automobile ac compressor via a BLDC motor instead of IC engine. This is only when the vehicle is parked. Now, I'm trying to determine torque requirement. Is my calculation correct? Power consumption: 1.46 kW compressor speed : 1000rpm...
  50. B

    Newton's method of estimation - using derivatives

    Homework Statement Newton devised the following method for approximating a real root of the equation f(x) = 0. i.e. a real number for which f(r) = 0. We begin by guessing an approximation, say x1, to the real root r. (i) Find the equation of the line tangent to the graph of y = f(x) at the...
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