diff --git a/slides/sections/3.md b/slides/sections/3.md index b0604b1..8f26aed 100644 --- a/slides/sections/3.md +++ b/slides/sections/3.md @@ -66,7 +66,7 @@ $$ $$ hence: $$ - Q_M(x) = -2 \ln \left[ \sqrt{2} \, \text{erf}^{-1} (1 - F_M(x)) \right] + Q_M(y) = -2 \ln \left[ \sqrt{2} \, \text{erf}^{-1} (1 - y) \right] $$ diff --git a/slides/sections/4.md b/slides/sections/4.md index 5c87d35..c61e48e 100644 --- a/slides/sections/4.md +++ b/slides/sections/4.md @@ -3,7 +3,8 @@ ## Sample parameters estimation -Once the points are sampled, how to estimate their median, mode and FWHM? +Once the points are sampled, +how to estimate their median, mode and FWHM? . . . diff --git a/slides/sections/5.md b/slides/sections/5.md index a250422..49845c2 100644 --- a/slides/sections/5.md +++ b/slides/sections/5.md @@ -14,7 +14,7 @@ FWHM $w_L\ex$ $w_M\ex (σ)$ ----------------------------------------------------- -## PDF parameters +## Moyal parameters A $M(x)$ similar to $L(x)$ can be found by imposing: @@ -37,7 +37,7 @@ $$ $$ -## PDF parameters +## Moyal parameters :::: {.columns} ::: {.column width=50%} @@ -50,7 +50,7 @@ $$ :::: -## Different medians +## Moyal parameters This leads to more different medians: @@ -60,7 +60,22 @@ This leads to more different medians: \end{align*} -## Samples +## Results compatibility -- Sample $L$: N = 50'000 points following $L_(x)$ -- Sample $M$: N = 50'000 points following $M_{\mu \sigma}(x)$ +Comparing results: + +$$ + p = 1 - \text{erf} \left( \frac{t}{\sqrt{2}} \right)\ \with + t = \frac{|x\ex - x\ob|}{\sqrt{\sigma\ex^2 + \sigma\ob^2}} +$$ + +- $x\ex$ and $x\ob$ are the expected and observed values +- $\sigma_e$ and $\sigma_o$ are their absolute errors + +. . . + +At 95% confidence level, the values are compatible if: + +$$ + p > 0.05 +$$ diff --git a/slides/sections/6.md b/slides/sections/6.md index e69de29..19117c0 100644 --- a/slides/sections/6.md +++ b/slides/sections/6.md @@ -0,0 +1,65 @@ +# Landau sample + +## Sample + +Sample N = 50'000 random points following $L(x)$ +$$ + L(x) = \frac{1}{\pi} \int \limits_{0}^{+ \infty} + dt \, e^{-t \ln(t) -xt} \sin (\pi t) +$$ + + +## Compatiblity results: + +Median: + +:::: {.columns} +::: {.column width=50%} + - $t = 0.761$ + - $p = 0.446$ +::: + +::: {.column width=50%} + $$ + \thus \text{Compatible!} + $$ +::: +:::: + +\vspace{10pt} + +. . . + +Mode: + +:::: {.columns} +::: {.column width=50%} + - $t = 1.012$ + - $p = 0.311$ +::: + +::: {.column width=50%} + $$ + \thus \text{Compatible!} + $$ +::: +:::: + +\vspace{10pt} + +. . . + +FWHM: + +:::: {.columns} +::: {.column width=50%} + - $t=0.495$ + - $p=0.620$ +::: + +::: {.column width=50%} + $$ + \thus \text{Compatible!} + $$ +::: +::::