# Cdf Python Example

Let's say you are building an air-flight time simulator. The gamma cdf is the regularized incomplete gamma function; the plain "gamma function" appears as a normalizing constant in the gamma density. Finally, use the PdfFileWriter object to write the output PDF. 1 Acceptance-Rejection Method As we already know, ﬁnding an explicit formula for F−1(y) for the cdf of a rv X we wish to generate, F(x) = P(X ≤ x), is not always possible. Since writing my original tutorial Python - NetCDF reading and writing example with plotting, I have received a lot of questions and feedback. This tutorial shows how to compute and plot an Empirical Cumulative Distribution Function (ECDF) in the R programming language. This app works best with JavaScript enabled. Heterogeneous Data ¶ One advantage that Statsmodels' KDEMultivariate has over the other algorithms is its ability to handle heterogeneous data, i. Uniform(a, b) [source] ¶ Uniform(a, b) represents a probability distribution with uniform probability density on the interval [a, b] and zero density everywhere else. We announce the public release of online educational materials for self-learners of CFD using IPython Notebooks: the CFD Python Class! Update! (Jan. The fact above implies that if X has CDF F, then F−1(U) will have CDF F. Mahalanobis distance is an effective multivariate distance metric that measures the distance between a point and a distribution. (This python executable is called ~peonyisi/bin/python. GitHub Issue Tracker. by row number and column number. 1 Sampling via Inversion of the cdf. 2019 Fire Season Outlook. It provides a high-level interface for drawing attractive and informative statistical graphics. pyplot as plt import numpy as np from mpl_toolkits. How to approximate the cdf of t-distribution efficiently? Approximation of t distribution is essential for finding the p-value in a computer program (while testing the hypothesis about the means). MVN）|Monte Carlo Note. Getting started with Python for science Note. In statistics and probability, many quantities are well modeled by the normal distribution, often called the "bell curve". A double-precision complex number is a complex number x + I*y with $$x$$, $$y$$ 64-bit (8 byte) floating point numbers (double precision). Example of a P-P plot comparing random numbers drawn from N(0, 1) to Standard Normal — perfect match. layouts import gridplot from bokeh. The probability density function of a Gaussian with mean $\mu$ and standard deviation $\sigma$ is: [math]f(x \; | \; \mu, \sigma^2) = \frac{1. Use the existing documentation. In the current version of Python-Docx (0. The examples below show how wrf-python can be used to make plots with matplotlib (with basemap and cartopy) and PyNGL. GitHub Issue Tracker. Python has an extensive, easy-to-use library of standard modules. A function to conveniently plot an empirical cumulative distribution function. By voting up you can indicate which examples are most useful and appropriate. data[name] # Attributes dictionary cdf. Let us generate a random sample of size 100 from beta distribution Beta(5, 2). cumulative distribution function. Example netCDF files. This shows the leave-one-out calculation idiom for Python. complex128 and np. statsmodels is a Python module that provides classes and functions for the estimation of many different statistical models, as well as for conducting statistical tests, and statistical data exploration. cdf(s, x) [source] ¶ Return the cumulative density function as an expression in x. 3 just because of my new computer is AMD64. y = binocdf(x,n,p) computes a binomial cumulative distribution function at each of the values in x using the corresponding number of trials in n and the probability of success for each trial in p. Anyway, here is what I came up with:. If you find this content useful, please consider supporting the work by buying the book!. These assumptions can be easily violated in time series by the addition of a trend, seasonality, and other time-dependent structures. gov Goddard Space Flight Center Software System Support O ce Code 610. This example also writes some of the netCDF data to an ASCII file. The module we will be using in this tutorial is PyPDF2. In the formulas that follow, "ln" always means "natural logarithm", while "log" always means "base 10 logarithm". We'll begin by providing some background information on probability distribution functions and the different ways in which you can sample random numbers from them in the COMSOL. This time, I'm going to focus on how you can make beautiful data visualizations in Python with matplotlib. InvF The inverse F distribution function with m and n degrees of freedom. The module we will be using in this tutorial is PyPDF2. Python - NetCDF reading and writing example with plotting. Here I'll show one very basic example but there are many more options for overlays, projections, colormaps, etc. None of these examples make use of xarray’s builtin plotting functions, since additional work is most likely needed to extend xarray in order to work correctly. Introduction¶. PythonForArmLinux. I find this form most useful, but some authors define the CDF in a simpler, less useful way. Fortunately, the cumulative standard normal distribution is included in the submodule of SciPy. Example Calculation: Calculations not provided here due to the number and ordering, they can be found in the attached workbook in the correct order with accompanying usage notes. plotting import figure, show, output_file def make_plot (title. There's even a huge example plot gallery right on the matplotlib web site, so I'm not going to bother covering the basics here. This plot shows the probability of finding a number in a bin or any lower bin. Let the CDF of Xbe F xand let be a uniform random variable on [0;1], then as long as Xis a continuous random variable its CDF will be invertible and hence X= F 1 x is a solution. Pythonのモジュールscipy. iloc – iloc is used for indexing or selecting based on position. from scipy. 6 (2,545 ratings) Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately. You will find a solution to this exercise in Cdf. You can use more than one paragraph, they must be separated by a line which contains a single hash mark #. title # get attribute value 'this is an example'. $\endgroup$ - Glen_b ♦ Jun 8 '17 at 0:50 $\begingroup$ @Glen_b thanks, I guess I want Gamma distribution. Welcome to Unidata. Similarly, the second example constructs an abelian group and assigns its generators to the letters a, b and c. matplotlib help: cumulative distribution histogram (self. The general idea is to take the model CDF equation and write it in such a way that a function of $$F(t)$$ is a linear equation of a function of $$t$$. Ok so it's about that time again - I've been thinking what my next post should be about and I have decided to have a quick look at Monte Carlo simulations. Let X 1,X 2, X 3 be a random sample from a distribution of the continuous type having pdf f(x)=2x, 0 [source] ¶ A binomial discrete random variable. 5 and the mean value of heads for 100 flips would be 50. netCDF arrays are handled using array objects provided either by the python numpy, Numeric or numarray packages. by row number and column number. This tutorial shows how to compute and plot an Empirical Cumulative Distribution Function (ECDF) in the R programming language. Accessing NetCDF datasets with Python - Part 1. data[name] # Attributes dictionary cdf. Properties. GitHub Gist: instantly share code, notes, and snippets. • Basic idea: Compare the CDF of your data to the CDF of a proposed model • Use quantiles to do this • Quantile is the value of such that • Sometimes expressed in terms of percentiles, e. Finv Computes the inverse of cdf at , with parameters and. I will refer to example file there as "example www files". complex128 and np. The gamma cdf is the regularized incomplete gamma function; the plain "gamma function" appears as a normalizing constant in the gamma density. The cumulative distribution function is applicable for describing the distribution of random variables either it is continuous or discrete. In this tutorial, you will discover how to check if your time series is stationary with Python. Use the joint m. method for computing the empirical cumulative distribution. For large values of n, the distributions should be the same. We calculate probabilities of random variables and calculate expected value for different types of random variables. I've compiled a recent version (2. and the cdf are 1-to-1, one can sample by first sampling and then solving for by inverting , or. cdfplot is useful for examining the distribution of a sample data set. Statistics and risk modelling using Python Eric Marsden Statistics is the science of learning from experience, particularly experience that arrives a little bit at a time. Note that in the formula for CDFs of discrete random variables, we always have , where N is the number of possible outcomes of X. lets see an example of each. And make sure you have checked the small example given in "examples" section before going on to next paragraph. Its value at any specified value of the measured variable is the fraction of observations of the measured variable that are less than or equal to the specified value. Tiny Python (archived link) - not to be confused with tinypy. In our example, the cdf evaluated at 7 is the probability of drawing 7 or fewer red marbles. In the example above, we first convert a small subset of Spark DataFrame to a pandas. netcdf4-python is a Python interface to the netCDF C library. There's even a huge example plot gallery right on the matplotlib web site, so I'm not going to bother covering the basics here. If you look at the sorted result, you'll realize that the smallest value represents 0% , and largest value represents 100 %. CDF software can transparently access data files in any encoding currently supported by the CDF library (For example: a CDF application running on a Sun can read and write data encoded in a VAX format. PyGSLIB was designed to. The following examples can be accessed with Polymath™, MATLAB™, or Wolfram CDF Player™. IDL, Matlab, and Python This tutorial makes use of the NetCDF4 package in Python. Create a new PdfFileWriter object. Plot a CDF for the values in fraction with 30 bins between 0 and 30%. Example Let’s. When placeholders { } are empty, Python will replace the values passed through str. title = 'this is an example' # set attribute type and value >>> d. First we need to import netCDF4-python, Numpy, Matplotlib for plotting, and Basemap for the map In : from netCDF4 import Dataset as NetCDFFile import matplotlib. y = binocdf(x,n,p) computes a binomial cumulative distribution function at each of the values in x using the corresponding number of trials in n and the probability of success for each trial in p. int64, respectively. The value can have its data type specified for the numeric data. com to assist learning in UK classrooms. First,download the miniconda packagefor your computer. By voting up you can indicate which examples are most useful and appropriate. and the cdf are 1-to-1, one can sample by first sampling and then solving for by inverting , or. You can vote up the examples you like or vote down the ones you don't like. 6, start by importing packages:. p = chi2cdf(x,v) computes the chi-square cdf at each of the values in x using the corresponding degrees of freedom in v. This channel is managed by up and coming UK maths teachers. In the next section, you will explore some important distributions and try to work them out in python but before that import all the necessary libraries that you'll use. Therefore, the graph of the cumulative distribution function looks something like this:. So let’s have a look at the basic R syntax and the definition of the ecdf command first:. Return to the Resources page. They are extracted from open source Python projects. ecdf import ecdf. x , n , and p can be vectors, matrices, or multidimensional arrays of the same size. Let us understand by using the following example. Let the CDF of Xbe F xand let be a uniform random variable on [0;1], then as long as Xis a continuous random variable its CDF will be invertible and hence X= F 1 x is a solution. describe(s) std=math. Before we go into examples, it will be best for us to understand further the object hierarchy of Matplotlib plots. Here is a simple example to be compiled with pdflatex -shell-escape:. Prepare example data. That is not the Mathematica CDF-format (Computable Document Format). norm¶ scipy. statsmodels. The general idea is to take the model CDF equation and write it in such a way that a function of $$F(t)$$ is a linear equation of a function of $$t$$. gives the multivariate cumulative distribution function for the distribution dist evaluated at { x 1 , x 2 , …. Compute the CDF of the sample. Let's assume that we have a random variable that follows a normal (Gaussian) distribution. asking questions about data • Suppose a factory claims to produce widgets with an average weight of 100g and a standard deviation of 22g • We receive a new shipment of widgets which seem oﬀ, and we want to see whether the. The cdf is a cumulative sum of all the probabilities lying in its domain and defined by: $cdf(x) = \sum_{k=-\infty}^{x} P(k)$ The idea of this processing is to give to the resulting image a linear cumulative distribution function. ECDF¶ class statsmodels. Normal Distribution CDF Normal Distribution is one of 'the' most applicable distribution in statistics. ndimage as ndi. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The cumulative distribution function, (c. ggplot is a plotting system for Python based on R's ggplot2 and the Grammar of Graphics. Scientists and researchers are likely to gather enormous amount of information and data, which are scientific and technical, from their exploration, experimentation, and analysis. Apache Spark Transformations in Python Examples Apache Spark Transformations in Python If you’ve read the previous Spark with Python tutorials on this site, you know that Spark Transformation functions produce a DataFrame, DataSet or Resilient Distributed Dataset (RDD). (This python executable is called ~peonyisi/bin/python. Tutorials on the scientific Python ecosystem: a quick introduction to central tools and techniques. The general idea is to take the model CDF equation and write it in such a way that a function of $$F(t)$$ is a linear equation of a function of $$t$$. Instructions. A cumulative probability is represented by a graph of the cumulative distribution function. 6; Python Data Analysis Library Pandas. Plotting Examples¶. These assumptions can be easily violated in time series by the addition of a trend, seasonality, and other time-dependent structures. iloc - iloc is used for indexing or selecting based on position. from mlxtend. from scipy. IncF The incomplete F-table function. Heterogeneous Data ¶ One advantage that Statsmodels' KDEMultivariate has over the other algorithms is its ability to handle heterogeneous data, i. x and v can be vectors, matrices, or multidimensional arrays that have the same size. For example, you can display the height of several individuals using bar chart. You can return to Part 1 (Post Processing Bismark Bisulphite Sequencing Data) or skip to Part 3 (Simple Visualisation of Bisulphite Sequencing Data). After completing this tutorial, you will know: The Student's t-test will comment on whether it is likely to observe two samples given that the samples were drawn from the same population. It shows the relationship between a numerical variable and a categorical variable. To follow this tutorial you may be familiar with: Python 2. Normal Distribution CDF Normal Distribution is one of 'the' most applicable distribution in statistics. The cumulative distribution function gives the cumulative value from negative infinity up to a random variable X and is defined by the following notation: F(x) = P(X≤x). Dash is an Open Source Python library which can help you convert plotly figures into a reactive, web-based application. The cdf is a cumulative sum of all the probabilities lying in its domain and defined by: $cdf(x) = \sum_{k=-\infty}^{x} P(k)$ The idea of this processing is to give to the resulting image a linear cumulative distribution function. You can overlay a theoretical cdf on the same plot of cdfplot to compare the empirical distribution of the sample to the theoretical distribution. For large values of n, the distributions should be the same. Let us understand by using the following example. As an instance of the rv_discrete class, binom object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution. Exponential and uniform distributions in Python. Here are some examples of Scipy. Functions related to probability distributions are located in scipy. format() method are essentially tuple data types and each individual value contained in the tuple can be called by its index number, which starts with the index number 0. basemap import Basemap. I will create examples of plotting data with: Pandas; Seaborn. ggplot is a plotting system for Python based on R's ggplot2 and the Grammar of Graphics. Histograms Histograms are useful for viewing (or really discovering)the distribution of data points. distributions. complex128 and np. A scalar input is expanded to a constant array with the same dimensions as the other input. Dist function, as follows:. Below is a simple example of a dashboard created using Dash. • When some observations are censored, we can estimate S(t) using the Kaplan-Meier product-limit estimator. How to compute the cumulative distribution functions and the percent point functions of various commonly used distributions in Excel, R and Python. It is built for making profressional looking, plots quickly with minimal code. And make sure you have checked the small example given in "examples" section before going on to next paragraph. plotting import figure, show, output_file def make_plot (title. start : this start is added to the sum of numbers in the iterable. By voting up you can indicate which examples are most useful and appropriate. These assumptions can be easily violated in time series by the addition of a trend, seasonality, and other time-dependent structures. The cumulative distribution function is applicable for describing the distribution of random variables either it is continuous or discrete. CDF(filename) as cdf: # All variable data loaded into dictionary in. CDF library includes a suite of tools that allow users to manipulate CDF files Provide read/write interfaces for C, FORTRAN, Java, Perl, C#/Visual Basic, IDL, MATLAB (and user-supplied software, e. Learn through real-world examples: Instead of sitting through hours of theoretical content and struggling to connect it to real-world problems, we'll focus entirely upon applied statistics. Maybe some other languages have better functionality for this task like MATLAB, Mathematica or R, and we could call them from Python? Worth investigating I think. a function to transform the cumulative proportions, for the Trellis-type usage of Ecdf. In time series terminology, we refer to this expectation as the time series being stationary. This module can read and write files in both the new netCDF 4 and the old netCDF 3 format, and can create files that are readable by HDF5 clients. sqrt(var) #note these are sample standard deviations #and sample variance values #to get population values s. netcdf4-python is a Python interface to the netCDF C library. We'll begin by providing some background information on probability distribution functions and the different ways in which you can sample random numbers from them in the COMSOL. var() will work #The location (loc) keyword specifies the mean. , the area under the normal distribution from negative infinity to x), given the upper limit of integration x, the mean, and the standard deviation. Statistics and risk modelling using Python 1. The general pattern is Example: scipy. from scipy. Seaborn is a Python data visualization library based on matplotlib. Kite is a free autocomplete for Python developers. netcdf), differing only slightly in their syntax. I would like to know how to improve it. sqrt() function when passed the expression a-b as an argument. The location (loc) keyword specifies the mean. DataFrame can have different number rows and columns as the input. If you’re a developer who wants to improve your understanding of Continuous Integration (CI) / Continuous Delivery (CD. It provides a high-level interface for drawing attractive and informative statistical graphics. meta[name][attr_name] # CDF variable information. , the area under the normal distribution from negative infinity to x), given the upper limit of integration x, the mean, and the standard deviation. Example import pysatCDF with pysatCDF. A couple of other options to the hist function are demonstrated. Its value at any specified value of the measured variable is the fraction of observations of the measured variable that are less than or equal to the specified value. $\begingroup$ Your file is in Common Data Format. (Note regarding your question: a cumulative distribution function is only ever used in the case of random variables--if the variables were deterministic, i. The entry point to programming Spark with the Dataset and DataFrame API. These assumptions can be easily violated in time series by the addition of a trend, seasonality, and other time-dependent structures. A SparkSession can be used create DataFrame, register DataFrame as tables, execute SQL over tables, cache tables, and read parquet files. This tutorial shows how to compute and plot an Empirical Cumulative Distribution Function (ECDF) in the R programming language. Let's say points are (x1,p1) & (x2,p2) where x1,x2 represent points on x-axi. I extract the round trip from each line and add it to an array called roundtriptimes. Know the deﬁnition of the probability density function (pdf) and cumulative distribution function (cdf). basemap import Basemap. Such random variables are infrequently encountered. Another alternative is Mayavy, but we find the Paraview is easier to install and more powerful. We calculate probabilities of random variables and calculate expected value for different types of random variables. Fueled by drought, an unprecedented buildup of dry vegetation and extreme winds, the size and intensity of these wildfires caused the loss of more than 100 lives, destroyed thousands of homes and exposed millions of urban and rural Californians to unhealthy air. The different chapters each correspond to a 1 to 2 hours course with increasing level of expertise, from beginner to expert. In python, we will apply 2-D convolution to two images, 'kitten. It will calculate the inverse of the normal cumulative distribution for a supplied value of x, with a given distribution mean and standard deviation. Scientists and researchers are likely to gather enormous amount of information and data, which are scientific and technical, from their exploration, experimentation, and analysis. Let’s take a normal RV as an example. For example:. You can vote up the examples you like or vote down the ones you don't like. Inverse Transform Sampling with Python Before we start with inverse transform sampling, let’s look at an example to build some motivation. A cumulative probability is represented by a graph of the cumulative distribution function. The following examples can be accessed with Polymath™, MATLAB™, or Wolfram CDF Player™. observed) data. Exponential and uniform distributions in Python. We announce the public release of online educational materials for self-learners of CFD using IPython Notebooks: the CFD Python Class! Update! (Jan. CDF_EPOCH is a single double(as float in Python), CDF_EPOCH16 is 2-doubles (as complex in Python), and TT2000 is 8-byte integer (as int in Python). Finally, use the PdfFileWriter object to write the output PDF. The following are code examples for showing how to use scipy. By voting up you can indicate which examples are most useful and appropriate. Binomial probabilities – examples (calculator) Once you have determined that an experiment is a binomial experiment, then you can apply either the formula or technology (like a TI calculator) to find any related probabilities. The cumulative distribution function can also be used to solve the probability of a range of outcomes. Below is a simple example of a dashboard created using Dash. In addition to custom CDF files for different target definitions, GeneChips and data analysis platforms, we also provide 1) a probe mapping file that matches individual probes in the custom CDF file and the corresponding Affymetrix CDF file; 2) a grouping file that can be used to find all targets (exons,. Python is an interpreted programming language with a design philosophy stressing the readability of code. statsmodels. In our previous Python Library tutorial, we saw Python Matplotlib. float64, np. Let’s say that that income of a company’s employees is normally distributed with mean of 10,000 USD and standard deviation of 1,000 USD. Given this knowledge, we can now define a function for plotting any kind of distribution. CREATE) # create dataset >>> d. In this example, we'll construct an Empirical cumulative distribution function to visualize the distribution of the data. CDF_TIME_TT2000 (TT2000 as short) is nanoseconds since J2000 with leap seconds. Calculations of the quantiles and cumulative distribution functions values are required in inferential statistics, when constructing confidence intervals or for the implementation of hypothesis tests, especially for the calculation of the p-value. Living Example Problems. For example, mvncdf(1,0,4) is the same as normcdf(1,0,2), where 4 is the variance and 2 is the standard deviation. For example, an appliance manufacturer investigates failure times for the heating element within its toasters. pyplot as plt import numpy as np from mpl_toolkits. layouts import gridplot from bokeh. Maybe some other languages have better functionality for this task like MATLAB, Mathematica or R, and we could call them from Python? Worth investigating I think. The speaker described a method for sampling from a probability distribution. Unlike R, a -k index to an array does not delete the kth entry, but returns the kth entry from the end, so we need another way to efficiently drop one scalar or vector. (This python executable is called ~peonyisi/bin/python. The function scipy. If you have any questions about how to perform 2-D convolution, refer to the example here. Generate random observations of a random variable X with a Gaussian distribution, mean and standard deviation Solution No closed-form expression exists for the cumulative distribution F x (x) of a Gaussian. Examples ## 5000 bootstraps using two cores bs=bootstrap(m_pl,no_of_sims=5000,threads=2) By default, the bootstrap function will use the maximum likelihood estimate to estimate the parameter and check all values of x min. lets see an example of each. Numpy Distributions and Statistical Functions: Examples + Reference Evaluate x on a Gaussian CDF. After completing this tutorial, you will know: The Student’s t-test will comment on whether it is likely to observe two samples given that the samples were drawn from the same population. The cumulative distribution function, (c. import numpy as np import scipy. This tutorial shows how to compute and plot an Empirical Cumulative Distribution Function (ECDF) in the R programming language. Example Python scripts that use LAMMPS. In the call to this function, we have to put the mean value: 1/lambda. name: Python str prepended to names of ops created by. This the standard procedure for opening, reading and saving a SAR image using PyRadar. I will refer to example file there as "example www files". This example also writes some of the netCDF data to an ASCII file. data data = cdf. Imagine we want to compare the distribution of two variables in our data. There's even a huge example plot gallery right on the matplotlib web site, so I'm not going to bother covering the basics here. After verifying the function logics, we can call the UDF with Spark over the entire dataset. We will learn the deﬁnition of beta distribution later, at this point we only need to know that this isi a continuous. sqrt(var) #note these are sample standard deviations #and sample variance values #to get population values s. Enter these factors in the binomial cumulative distribution function calculator to find the binomcdf function. First we need to import netCDF4-python, Numpy, Matplotlib for plotting, and Basemap for the map In : from netCDF4 import Dataset as NetCDFFile import matplotlib. In our previous Python Library tutorial, we saw Python Matplotlib. Videos designed for the site by Steve Blades, retired Youtuber and owner of m4ths. Inputs and Setup: Either use the existing [Z-Score] parameter or replace with your output for Z-Score. pyplot as plt import numpy as np from mpl_toolkits. In summary, the cumulative distribution function defined over the four intervals is: The cumulative distribution function is therefore a concave up parabola over the interval −1 < x ≤ 0 and a concave down parabola over the interval 0 < x < 1. cdf gives the cumulative distribution function for the distribution dist evaluated at x. Histograms Histograms are useful for viewing (or really discovering)the distribution of data points. sum(iterable, start) iterable : iterable can be anything list , tuples or dictionaries , but most importantly it should be numbers. DataFrame can have different number rows and columns as the input. Scipy is a Python open source package used for the scientific computing across many domains such as engineering, mathematics, sciences etc. cdf gives the cumulative distribution function for the distribution dist evaluated at x. A cumulative probability is represented by a graph of the cumulative distribution function. Tutorial: Basic Statistics in Python — Probability When studying statistics for data science, you will inevitably have to learn about probability. 2019 Fire Season Outlook. In example 7. netCDF-3 software reads and writes data in only the XDR data encoding, but netCDF-4. cdfplot is useful for examining the distribution of a sample data set. The fact above implies that if X has CDF F, then F−1(U) will have CDF F. Again, I would recommend you to read the wikipedia page on Histogram Equalization for more details about it. This part of the Jenkins User Documentation contains a series of introductory tutorials to help you begin building your applications in an automated fashion with Jenkins. How to approximate the cdf of t-distribution efficiently? Approximation of t distribution is essential for finding the p-value in a computer program (while testing the hypothesis about the means). The cumulative distribution function gives the cumulative value from negative infinity up to a random variable X and is defined by the following notation: F(x) = P(X≤x). These may be useful to developers of netCDF tools who want to test their tool on real data rather than small artificial examples.