Mann-Kendall monotonicity test python

The Mann-Kendall test is a non-parametric statistical test used to determine if there is a monotonic upward or downward trend in a dataset over time. In Python, the Mann-Kendall test can be implemented using the `mk_test()` function from the `pymannkendall` library.

Here's an example of how to use the `mk_test()` function to perform a Mann-Kendall test on a dataset:

import numpy as np
from pymannkendall import mk_test

# Generate some random data
data = np.random.rand(100)

# Perform the Mann-Kendall test
trend, h, p, z, Tau, s = mk_test(data)

# Print the results
print(f"Trend: {trend}")
print(f"p-value: {p}")

In this example, we first generate a random dataset of 100 values using NumPy's `random.rand()` function. We then pass this dataset to the `mk_test()` function, which returns several values:

- `trend`: The type of trend observed in the dataset (0 = no trend, 1 = upward trend, -1 = downward trend)
- `h`: A binary indicator of statistical significance (0 = not significant, 1 = significant)
- `p`: The p-value of the test
- `z`: The normal test statistic
- `Tau`: The Kendall rank correlation coefficient
- `s`: The score of the test

Finally, we print the `trend` and `p` values to the console. If the p-value is less than 0.05, we can conclude that there is a statistically significant trend in the dataset.