# What is Estimate: Definition and 375 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. ### POTW Estimate of a Principal Value Integral

For ##x\in \mathbb{R}##, let $$A(x) = \frac{1}{2\pi}\, P.V. \int_{-\infty}^\infty e^{i(xy + \frac{y^3}{3})}\, dy$$ Show that the integral defining ##A(x)## exists and ##|A(x)| \le M(1 + |x|)^{-1/4}## for some numerical constant ##M##.
2. ### A A possible estimate for the fourth central moment

A possible estimate for the third central moment is the product of the skewness and the standard deviation raised to the third power. Is it also true that a possible estimate for the fourth central moment is the product of the kurtosis and the standard deviation raised to the fourth power?
3. ### Parasitic Inductance, rough estimate -Single cable through steel

DC case - but customer ran their cable run through a couple boxes, this would not be allowed in AC due to the eddy current created in fittings and the enclosure steel. ( I do not even know if code would allow this for DC) - but anyway. This is part of a high power dc system and I suspect the...
4. ### How to Estimate Pi Without Trig Functions

Have neither seen an estimation nor derivation of pi that does not use trig functions. This is problematic as trig functions require radian inputs, via the relation pi radians = 180 deg. But if looking for pi, then how to get the input for the trig functions without pi? Sure there are...
5. ### I Is the Sample Size Calculation in This Article Accurate?

Hello! I will present an article tomorrow and I just found out the sample size calculation could be wrong (it's not my article). It's very urgent, if someone could help me to confirm if the sample size calculation is right or wrong (and if so, help me to calculate the correct amount) this would...
6. ### MHB Point Estimate, Margin of Error and Confidence Level

1. One of the few negative effects of quitting smoking is weight gain. The data below shows the weight gain (in pounds) of 18 respondents 12 months after they quit. If the mean gain follows a normal distribution with a standard deviation of 9 pounds, estimate the mean weight gain of the 18...
7. ### Calculate the pooled estimate of variance

OK, Let me attempt part (i), first, Here we have; ##s^2_p ##=##\dfrac{ (n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}## ##s^2_p ##=##\dfrac{ (7-1)0.63953+(7-1)0.6148}{7+7-2}## ##s^2_p ##=##\dfrac{3.83718+3.6888}{12}## ##s^2_p ##=##\dfrac{3.83718+3.6888}{12}## ##s^2_p ##=##\dfrac{7.52598}{12}##...
8. ### I Back of the envelope estimate, energy flow in a box of plasma

Say we look at a spherical region of the sun where energy is mainly transported by radiation. Say this happens between some particular radius R and R + dr. Let the temperature at R be giving by T(r). At this particular radius let the gravitational acceleration be a reasonably well know function...
9. ### Popular estimate of the Earth's atmosphere possibly wrong?

So I just realized that on the internet the number that frequently pops up with regards to the total mass of the Earth's atmosphere is 5,100,000,000,000,000,000 kilograms. For example, the number is mentioned two times on the Wikipedia page for the Earth's atmosphere, there are more examples...
10. ### B How to estimate the heating power of warm air entering a room?

In winter I heat my workshop with a radiant heater and an oil heater. Easy to know how much heat is entering the room. But in spring and summer I don't use those; I blow hot air from the ceiling cavity into the room, and I was wondering how I would estimate the heating power and the formula to...
11. ### I How is the popular estimate of the Earth's atmospheric mass correct?

There is a number floating around on the internet that says that the mass of the Earth's atmosphere is about 5 quintillion kilograms. The way that that number was calculated was through knowing that per square meter of surface area at sea level, about 100,000 Newtons of force is applied, which...
12. ### Estimate the following quantities from a graph of the refractive index of NaCl

a) I managed to obtain some results that are roughly around what is given in the answers. Because \varepsilon_{st} and \varepsilon_{\infty} are values of \varepsilon_{1}, I used this approximation: n\approx \frac{1}{\sqrt{2}} (\varepsilon_{1}+\sqrt{\varepsilon_{1}^2})^{1/2} -> \varepsilon_{1} =...

If I have a source of radioactivity that is concentrated instead of evenly spread out, like a "tablet" source instead of a evenly distributed aerosol/dust on ground for example then is it possible to even estimate the total number of disintegrations (Becquerels per second) by measuring the...
14. ### A Minimum sample length to estimate the frequency of a sinusoid

Given a discretely sampled horizontal sinusoid of length p, and unknown amplitude, what is the minimal number of consecutive points on a window that is required to correctly estimate its total length, starting at any random point on the wave? Initially I would think it would be either p (full...
15. ### Electrical How to estimate friction on the bearings to select motor?

I'm willing to build a motorized gimbal head for my camera (something like this: https://www.amazon.com/dp/B01JN5D40A/?tag=pfamazon01-20). If my understanding is correct, given that camera will be well balanced on the platform, the motors would not need to hold the load and only should be...
16. N

### Estimate Revenue Per Share

The revenue per share for Twitter, Inc. was $1.17 in 2013 and$3.25 in 2015. Use the Midpoint Formula to estimate the revenue per share in 2014. Assume that the revenue per share followed a linear pattern. (Source: Twitter, Inc.) This is an exercise using the midpoint formula. I just want to...
17. ### How to estimate the interaction time of Raman scattering?

Maybe we could use (1) uncertainty principle $\Delta E \Delta t = \hbar$ and get $\Delta E$ from the spetrum. Or (2) forced vibration model, then get the damping factor $\gamma$， and get $Delta t = frac{1}{\gamma}$
18. ### How would one estimate the rotation period of a star from its spectrum

The figure is shown; the measurements were taken on two consecutive observing nights. The Ordinate is the flux normalized to continuum and the abscissa is the wavelength scale. You can see the "bumps" indicated by the arrows referring to some Starspot as the spot moves on the profile; assuming a...
19. ### Lotka Volterra estimate parameters from experimental data

Namely, in the system, I have obtained the value of parameters L, M, A and D, because I treat the other organism as equal to zero, i.e., it doesn't exist, but I am struggling about the values of B and C, that are coupled with the product of x and y. Can anyone help me how to obtain those values...
20. ### Estimate the initial velocity of the cars after the collision

What came to my mind for this question is: Consider one of the cars. The velocity and mass of this car are V and M respectively. And the velocity and mass of the piece attached to the car are m, v respectively. Before the collision, the velocity of this piece relative to this car is zero. So its...
21. ### MHB How to estimate simplex gradient using Taylor series?

I read Iterative methods for optimization by C. Kelley (PDF) and I'm struggling to understand proof of Notes on notation: S is a simplex with vertices x_1 to x_{N+1} (order matters), some edges v_j = x_j - x_1 that make matrix V = (v_1, \dots, v_n) and \sigma_+(S) = \max_j \lVert...
22. ### Estimate the partition function by analyzing a graphic

I am not sure, but since the partition function Z is just the sum of all Boltzmann Factor We can just add: (some terms don't appear in the image, by the way, the estimative is nice, the result is above ANS) But i didn't understand what the author did: While i didn't even care about the...
23. ### How to estimate the measurement uncertainty of an oscilloscope ?

I have an Textronics oscilloscope with 500 MHz sampling rate and using an 50 ohm cable for the measurement. I can’t find the measurement uncertainty in the manual or the calibration sheet. In the calibration sheet it says an ‘uncertainty’ for the used channel in divisions, for example 1m up to...
24. ### I Estimate the magnitude of a line integral exp(iz) over a semicircle

Not homework, just trying to understand a statement in the book. On page 158 in Fisher, the following statement is made: In these applications of the Residue Theorem, we often need to estimate the magnitude of the line integral of e^{iz} over the semicircle = Re^{i\theta}, \; 0 \le \theta \le...
25. ### Lab Experiment: Estimate the error in these measurements of Ohm's law

Hi, I have measured a set of V-I values, and I have to provide the value of the resistance. I have used ac and dc current. The circuit was quite simple: power supply -> ammeter -> resistance -> [power supply] wave generator -> ammeter -> resistance -> [wave generator] Voltage was measured...
26. ### MHB Probability distribution: Estimate the size of the fox population

In a park , 200 foxes are tagged. In 100 sighting, 14 were tagged. Estimate the size of the fox population ? This is how approached . 200 tagged : Population 14 tagged : 100 (200x100/14)= Estimated Population = 1,429 I wonder if this is right !
27. ### Realistic Core Weight Reduction for 1000Hz Freq in 100KW DC/DC Converter

I have a customer looking for a 100KW isolated DC/DC converter. What is a realistic transformer core weight reduction if we get 1000Hz fundamental. Assume a 60Hz core is 300 Lbs, how much smaller could a 1kHz Core be?
28. ### MHB 2.7.2 AP Calculus Exam .... distance traveled estimate

https://www.physicsforums.com/attachments/9542 ok all I did was count squares so about 21
29. ### MHB Estimate Paint Amount for Hemispherical Dome w/ Differentials

First I list what I am given: Diameter: 46m DR: 0.0003m (converted from the 0.03cm that was given) DV: ? Volume of a Sphere = 4/3 pi r^3 But volume of a half a Sphere = 2/3 pi r^3 And Radius = Diameter/2 So...dv = 2 pi (23m)^2 (0.0003m) Using a Calculator I am given 0.3174. The question asks...
30. ### Clausius-Clapeyron equation to estimate sublimation pressure of water

Before this question, the questions were about the Clapeyron equation, and how to estimate ##\Delta s##. I'm completely put off by this question however, and don't know where to start. I've found that the triple point of water is at ##0.01°C##, and there is indeed data in the table for...
31. ### Estimate the temperature change due to vaporizing liquid

I'm releasing pressurized propellant into another chamber which is at atmospheric pressure, I want to estimate the temperature to which that chamber will drop to and the rate at which the liquid (collecting in the new chamber) will boil. The second chamber is open to atmosphere via a small...
32. ### Estimate the mass of the water (Carnot cycle)

m=Q/c(79*ln80)
33. ### How to estimate the heating of a wire

Hello, I've done some background research on this, and answers seem to vary. I would like to calculate the amount of heating in a wire. Let's say I want to heat a wire up to 60 degrees. I have 1 W of power and 150 mA of current at my disposal to do so. How could I estimate the wire diameter...
34. ### How to estimate a constant drag coefficient of a boat?

Hi there, I have modeled with MAXSURF a few variations of a prehistoric logboat in order to test a few theories. Now, I am trying to look at resistance-performance over a range of speed. To do so, I need to include a constant drag coefficient without knowing the drag force and velocity (both...
35. ### A Estimate the source of a variable when there are several distributions

Hello everyone In my study, I inject a different amount of fluid in each experiment, such as 1 ml, 2 ml..., and test the change in the general dielectric properties of the solution. Now that I have done much (over 100) measurements for each injection in a specific volume, one can see that for...
36. ### How to estimate the time it takes to generate steam?

Hello people, I have a question regarding the time calculation. could you please let me know if there are any equations with which I can find the time to generate steam in the header for certain pressure level. lets say I am supplying fuel and mass flow of water to the boiler at certain...
37. ### How to estimate the performance of a pump using Navier Stokes?

Hello everyone, Attached is the homework problem (FluidHmk.PNG) as well as the attempt (Attempted 1 and 2). Just wanted to know if this is method to approach the problem Thanks in advance.
38. ### How to estimate a GARCH model in python (without standard function)?

Hi, I want to program an GARCH model for exchange rates. To do this, I calculated the residuals. Next, I did the following (in python) def main(): vP0 = (0.1, 0.05, 0.92) a = minimize(garch_loglike, vP0, eps, bounds = ((0.0001, None), (0.0001, None), (0.0001, None))...
39. ### Trapezoidal rule to estimate arc length error

I got the first part of it down, $$L=\int_1^5 \sqrt{1+(\frac{1}{x^2})}dx$$ I just want to know if it's right to make your ##f(x)=\sqrt{1+\frac{1}{x^2}}## then compute it's second derivative and find it's max value, for the trapezoidal error formula.
40. M

### I Error estimate for iterative convergence

On the following page on wikipedia: https://en.wikipedia.org/wiki/Fixed-point_iteration the section "Examples" has a second bullet point, where the author suggests ##q=0.85##, but how did they get this number? I tried googling everything and could not find out how ##q## is determined.
41. ### Estimate the number of pixels in an image

Homework Statement The physical size of a single LOFAR station, operating at 150MHz is about 50m. Estimate the number of pixels which would be needed to map the full primary beam if one wished to include all LOFAR stations (maximum baseline ~ 800 km) at full resolution. Homework Equations...
42. ### Can a Web Developer Fix Out-of-Profession Software Issues?

Can a programmer "for example a web developer" understand the code and algorithm of a program which is out of his profession for example an office program stopped working or a menu/function of that office program does not work, can a web developer estimate the problem and fix it or only he can...
43. ### Simpson's method, error estimate

Homework Statement Hello, using Simpson´s method, one can calculate the number of intervals needed to achieve a given accuracy, through the error formula. Is there any other way to know that the required accuracy is achieved other than computing the integral and comparing it to the result from...
44. ### What is the estimated top speed of a modified 65 Mustang SIX-Cylinder?

Using on-line formulas I show my modified 65 Mustang SIX-Cylinder can reach 122 MPH...don't think so! I understand outside forces act on a moving object, requiring more force to act against that force, to increase speed. I am old and not an engineer, so please excuse me if I use wrong terms, but...
45. ### I Estimate of ground state energy for the Yukawa potential

I’ve seen the uncertainty principle used to calculate the ground state energy for things like hydrogen and the harmonic oscillator, but can this be done for the Yukawa potential where you have an exponential?
46. ### I How to estimate total energy when dealing with beamsplitters

I'm having a brain freeze right now and I need some help. :frown: I have a 50/50 beamsplitter (non-polarizing) with 5% tolerance. Test measurement (with a laser at a certain wavelength) gave that I'm transmitting 5.36 units and reflecting 4.6 units (49.5 transmitted; 42.6% reflected). Units...
47. ### Estimate of the greatest possible radius of a rocky planet

Homework Statement "Given a certain rocky material, estimate the greatest possible radius of a planet made up of said material" Homework Equations ##P = \frac{2}{3}\pi G\rho^2R^2## ##R = \frac{1}{\rho}\sqrt{\frac{3P}{2\pi G}}## The Attempt at a Solution I'm not quite sure of the validity of...
48. ### What Is the Correct Method to Estimate Ionization Energy in He-like Carbon?

Homework Statement In He-like Carbon, C V, the excitation energy of 1s3s ##^1S## is 2851180 ##cm^-1## and for 1s4s ##^1S## it is 2988246 ##cm^-1##. Estimate the ionization energy. Compare with the value in the NIST database! Homework Equations ##E_{io}= T + E_{excitation}, ## ##T =...
49. ### Estimate for the change in range for a proton

Homework Statement I've uploaded the question in the attached file. Homework Equations R ∝ 1/p R ∝ M/z2 The Attempt at a Solution I don't understand what is in my lecture notes. What equations do I need to attempt this question? Thank you.
50. ### MHB Construct the 99% confidence interval estimate

A simple random sample of 400 high school football players was taken in order to estimate the mean weight of all high school football players. The sample has a mean of 198 lbs. and a standard deviation 26 lbs. Construct the 99% confidence interval estimate of the mean weight of all high school...