Isaac Barry

2022-09-04

Working on a problem related to effect size, I get this relation where

$Q=\mathrm{log}(m)(m-\frac{1}{m})$

The domain of $m$ is $]0,\mathrm{\infty}[$. For a given $Q$, whenever I find a $m={m}^{\ast}$ satisfying the equality, the equality is also satisfied with $m=1/{m}^{\ast}$. Therefore, I can limit the domain of $m$ to $]1,\mathrm{\infty}[$.

Is there a formula that can isolate $m$ so that given a value $Q$ ($Q\in {\mathbb{R}}^{+}$), $m$ follows?

$Q=\mathrm{log}(m)(m-\frac{1}{m})$

The domain of $m$ is $]0,\mathrm{\infty}[$. For a given $Q$, whenever I find a $m={m}^{\ast}$ satisfying the equality, the equality is also satisfied with $m=1/{m}^{\ast}$. Therefore, I can limit the domain of $m$ to $]1,\mathrm{\infty}[$.

Is there a formula that can isolate $m$ so that given a value $Q$ ($Q\in {\mathbb{R}}^{+}$), $m$ follows?

Joel Reese

Beginner2022-09-05Added 17 answers

There are only two solutions for a given $Q$. If you want to solve the equation using iterative method would work

${m}_{n+1}=\frac{\mathrm{log}({m}_{n})({m}_{n}^{2}-1)}{Q}$

Use an initial guess ${m}_{0}$ in $(0,1)$. As this will make sure that square term doesn't explode. You can get arbitrary accuracy from this.

${m}_{n+1}=\frac{\mathrm{log}({m}_{n})({m}_{n}^{2}-1)}{Q}$

Use an initial guess ${m}_{0}$ in $(0,1)$. As this will make sure that square term doesn't explode. You can get arbitrary accuracy from this.

What is the range of the function $y={x}^{2}$?

The domain and range of $y=\mathrm{sin}x$ is

A)$R,[0,\mathrm{\infty}]$

B)$R,[-1,1]$

C)$R,[-\mathrm{\infty},\mathrm{\infty}]$

D)$R,[1,\mathrm{\infty}]$Mean of the squares of the deviations from mean is called the:

Variance

Standard deviation

Quartile deviation

ModeHow to evaluate P(10,2)?

What is the effect of wind speed on evaporation?

What is the range of a linear function?

Find the range of $\frac{{x}^{2}}{1-{x}^{2}}$

State the main limitations of statistics.

What is the range of the function y = x?

Tell whether the statement is true or false : A data always has a mode.

In most cases,_____variables are not considered to be equal unless they are exactly the same.

A local newspaper in a large city wants to assess support for the construction of a highway bypass around the central business district to reduce downtown traffic. They survey a random sample of 1152 residents and find that 543 of them support the bypass. Construct and interpret a 95% confidence interval to estimate the proportion of residents who support construction of the bypass.

$3+3x3-3+3=?$What is the right answer and how?

Define lateral displacement.