Have added example pictures

Check here (2012)

https://stats.stackexchange.com/questions/27861/similarity-measures-between-curves

for a whole variety of approaches (a range of many different approaches).

Steftcho P. Dokov thank you for the stack exchange link. It focuses on computing the similarity between two ordered sets of points. In my case, comparing a blue set to another blue set works. I am however to compare the shapes of both curves from one 2D space to another. If I simply take both sets and compare curve versus curve between each spaces (blue vs blue and red vs red), I do not think its sufficient. Results would not be accurate because this method does not take into consideration the relationship between the two curves in one 2D set compared to other?

Makes sense?

Yes, make sense. It looks like you may need using "Procrustes analysis" https://en.wikipedia.org/wiki/Procrustes_analysis

which is mentioned at the stack exchange link.

Furthermore, perhap you can do the statistical Kolmogorov-Smyrnov test for goodness-of-fit in 2-d case

https://www.google.com/search?q=kolmogorov+smirnov+test+in+two-dimensions

e.g., in matlab

https://www.mathworks.com/matlabcentral/fileexchange/48309-2-d-kolmorogov-smirnov-test-n-d-energy-test-hotelling-t-2-test

% kstest2d Two-dimensional, 2-sample Kolmorogov-Smirnov test

%

% [p,D] = kstest2d(s1,s2);

%

% Compare two, 2-dimensional distributions using Fasano & Franceschini's

% generalization of the KS-test.

%

% The analytic distribution of the statistic is unknown, and p-values

% are estimated using an approximation (Press et al., 1992) to FF's Monte

% Carlo simulations.

%

% INPUTS

% s1 - [n1 x 2] matrix

% s2 - [n2 x 2] matrix%

% OUTPUTS

% p - approximate p-value

% D - K-S statistic

Hopefully, this helps.

Good luck

thank you for help Steftcho P. Dokov . ill take a look into it.

Does the first chart have X as time still?

Simon AA Davis yes it has.

There are several ways to compare two curves to other two curves, depending on the specific aspects you want to analyze. Here are some common approaches:

Visual Comparison:

• Overlay the curves on a single plot: This is the simplest method and allows you to visually assess similarities and differences in shapes, trends, and relative positions.
• Color-code the curves: This helps distinguish between the four curves and identify overlapping sections.

Quantitative Comparison:

• Calculate summary statistics: Compute measures like mean, median, standard deviation, minimum, and maximum values for each curve.
• Compare slopes: If the curves represent functions, calculate the slopes at different points to compare their rates of change.
• Calculate areas between curves: This can be useful if you're interested in the magnitude of the difference between the curves. Numerical integration techniques can be used for this purpose.

Statistical Tests:

• Similarity metrics: Depending on your data, you can use metrics like Root Mean Squared Error (RMSE) or Mean Absolute Error (MAE) to quantify the difference between two curves.
• Statistical hypothesis testing: Formal statistical tests can be used to determine if the observed differences between the curves are statistically significant or simply due to random chance.

Advanced Techniques:

• Curve fitting: Fit mathematical functions to each curve and compare the resulting parameters.
• Dynamic Time Warping (DTW): This technique allows for comparison of curves that have different lengths or are misaligned in time.

Choosing the right method depends on several factors:

• The nature of the data: Are the curves representing continuous functions, discrete data points, or something else?
• The specific aspects you want to compare: Are you interested in overall shape, specific features, or the difference between them?
• The desired level of detail: Do you need a simple visual comparison or a more statistically rigorous analysis?

Here are some additional tips:

• Clearly define what you want to compare: Before applying any method, be clear on what aspects of the curves you are interested in comparing.
• Consider scaling the data: If the curves have different scales, consider normalizing them before comparison to prevent one curve from dominating the analysis.
• Use appropriate software tools: Depending on your chosen method, various data analysis software packages can help with calculations and visualizations.

By combining these techniques and considering your specific goals, you can effectively compare two curves to other two curves and gain valuable insights from your data.

Adnan Majeed Thank you for extensive answer. I am searching for Quantitative Comparison solution. I need to find similarity between shape formed by two curves on one 2D space compared to shape formed by other two curves on second 2D space.

The nature of the data represents discrete data points in time on both 2D spaces.

Calculating area between two curves is not a suitable solution as the shape is not taken into consideration.