# [R] 2 dimensional Measure of Smoothness/ Hurst Exponent questions

From: xiang li <lixiang128_at_gmail.com>
Date: Fri, 08 Apr 2011 15:58:43 -0500

Dear R users:

In my research I need to come up with a method to measure the smoothness for a closed curve (looks like ellipse, but actually not). I was working on calculating Hurst Exponent using 2 dimensional dataset.

I checked fArma, Randomfields and several functions in fractal packages, but could not find a way to calculate Hurst Exponent for 2 dimensional data. For example, in fArma package, rescaled method is defined as rsFit(x, levels = 50, minnpts = 3, cut.off = 10^c(0.7, 2.5), doplot = FALSE, trace = FALSE, title = NULL, description = NULL). But I need to input 2 variables instead of one.

An example dataset a:
Obs Day Hour Ta Tb

```121  20    0 15.72917 38.72908
122  20    1 15.22833 38.72137
123  20    2 14.58000 38.70560
124  20    3 13.92000 38.71345
125  20    4 13.54167 38.69884
126  20    5 13.71583 38.64483
127  20    6 15.16667 38.61158
128  20    7 16.92333 38.60596
129  20    8 17.81167 38.61342
130  20    9 18.76250 38.60460
131  20   10 19.84833 38.60891
132  20   11 20.53583 38.57431
133  20   12 23.00750 38.60031
134  20   13 26.49583 38.60715
135  20   14 23.42250 38.61355
136  20   15 26.01417 38.64173
137  20   16 26.76500 38.66624
138  20   17 24.54917 38.66912
139  20   18 23.67833 38.67209
140  20   19 23.20083 38.67061
141  20   20 22.12750 38.68486
142  20   21 20.42083 38.72173
143  20   22 19.25083 38.70809
144  20   23 17.44417 38.73694

```

You can run: plot(x=a\$Ta,y=a\$Tb,type="l") to see the curve. Could someone help me to find a way to measure the smoothness of this curve? Or could you teach me how to calculate H for 2 dimensional dataset? Thank you so much for your help. I really appreciate!

Xiang

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