Skip to main content

probability or statistics - How to partition a list into sublists in a similar way to Histogram


I have a list of list as below (I show part of it)


{{1902, 0.4662}, {1903, 0.22443}, {1905, 0.02936}, {1906, 

  0.02702}, {1908, -0.08354}, {1909, -0.05241}, {1911, 
  0.02388}, {1912, 0.03738}, {1914, 0.25015}, {1915, 0.2831}, {1917, 
  0.4415}, {1919, 0.18315}, {1921, 0.2256}, {1923, 0.24132}, {1926, 
  0.21473}, {1928, 0.29596}, {1930, 0.47693}, {1933, 0.41607}, {1935, 
  0.22161}, {1937, 0.3322}, {1940, 0.2099}, {1942, 0.23376}, {1944, 
  0.44114}, {1947, 0.15876}, {1949, 0.43953}, {1951, 0.71407}, {1954, 
  0.9595}, {1956, 0.59436}, {2000, 0.6832}, {2004, 0.86861}, {2007, 
  0.48201}, {2011, 0.70796}, {2015, 0.57029}, {2020, 0.61997}, {2026, 
  0.79266}, {2032, 0.78726}, {2038, 0.83884}}


For example, in {1902,0.4662} "1902" represent time 19:02 and 0.4662 represent the data at time 19:02.


What I want to do is to calculate average of the data in every 5 minutes. That is from 19:02 to 19:06, from 19:07 to 19:11. Notice the time step is not evenly distributed.


Histogram can naturally count how many of the data are in each interval. I want to partition the list like Histogram and then I can calculate average in each interval. And notice that the data may not be in a single day.


I can't figure out an elegant way to do this with built-in function. Can somebody help me?


Besides I think this is a very simple statistical calculation of data. I want to know what software could do this easily and directly.


Update: the full data sample is here http://en.textsave.org/VdL with date information



Answer



One approach:





  1. Create intervals from dataset;


    int = Table[Interval[{j, j + 4}], {j, 1902, 2038, 5}];


  2. Calling your dataset data the means for the desired intervals can be obtained:


    Mean /@ GatherBy[data, IntervalMemberQ[int, #[[1]]] &][[All, All, 2]]


yielding:




{0.186753, -0.0373567, 0.19021, 0.283417, 0.228025, 0.386445, 
0.31884, 0.27105, 0.33745, 0.437453, 0.77693, 0.6832, 0.86861, 
0.594985, 0.57029, 0.61997, 0.79266, 0.78726, 0.83884}

EDIT


Mr. Wizard correctly pointed out the error in my code. My first edit was wrong. The easiest approach (it seems to me) is to convert times to temporal data.


f[x_] := {2013, 9, 28, IntegerPart[x/100], 
  100 (x/100 - IntegerPart[x/100])}

Then using TemporalData



td = TemporalData[{f[#[[1]]], #[[2]]} & /@ data];
answ = TemporalData`Aggregate[td, {5, "Minute"}]

The default function applied to the partitioned temporal data is mean.


This can be visualised:


DateListPlot[{td["Path"], answ["Path"]}, Joined -> {False, True}]

A good post is here.


enter image description here


Comments

Post a Comment

Popular posts from this blog

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]
Post a Comment
Read more

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]
Post a Comment
Read more

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.
Post a Comment
Read more