Concept

Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable , or just distribution function of , evaluated at , is the probability that will take a value less than or equal to . Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by a right-continuous monotone increasing function (a càdlàg function) satisfying and . In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to . Cumulative distribution functions are also used to specify the distribution of multivariate random variables. The cumulative distribution function of a real-valued random variable is the function given by where the right-hand side represents the probability that the random variable takes on a value less than or equal to . The probability that lies in the semi-closed interval , where , is therefore In the definition above, the "less than or equal to" sign, "≤", is a convention, not a universally used one (e.g. Hungarian literature uses "

Official source

https://en.wikipedia.org/wiki/Cumulative_distribution_function

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related courses (32)

CS-401: Applied data analysis

This course teaches the basic techniques, methodologies, and practical skills required to draw meaningful insights from a variety of data, with the help of the most acclaimed software tools in the data science world (pandas, scikit-learn, Spark, etc.) ...

PHYS-467: Machine learning for physicists

Machine learning and data analysis are becoming increasingly central in sciences including physics. In this course, fundamental principles and methods of machine learning will be introduced and practised. ...

PHYS-512: Statistical physics of computation

The students understand tools from the statistical physics of disordered systems, and apply them to study computational and statistical problems in graph theory, discrete optimisation, inference and machine learning. ...

Related MOOCs (2)

Plasma Physics: Introduction

Plasma, the fourth state of matter, is by far the most abundant form of known matter in the universe. Its behavior is very different from the other states of matter we are usually familiar with. To understand it, a rigorous formalism is required. This is essential not only to explain important astrophysical phenomena, but also to optimize many industrial and medical applications and for achieving fusion energy on Earth. This physics course, taught by world-renowned experts of the field, gives you the oppor

Intro to Traffic Flow Modeling and Intelligent Transport Systems

Travelers in large cities experience significant congestion during their everyday trips. Expanding roads and infrastructure is not a long-lasting remedy to urban congestion. This course will focus on understanding traffic congestion and will explore ways to improve mobility through advanced traffic management schemes. As we all experience, congestion is a highly complex process without a single explanation. An interesting question is: “Can we describe these complex interactions with simple and elegant ways?

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Official source

https://en.wikipedia.org/wiki/Cumulative_distribution_function

About this result

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related courses (32)

CS-401: Applied data analysis

PHYS-467: Machine learning for physicists

PHYS-512: Statistical physics of computation

Related lectures (32)

Fundamental Limits of Gradient-Based Learning

Delves into the fundamental limits of gradient-based learning on neural networks, covering topics such as binomial theorem, exponential series, and moment-generating functions.

Collisionless Boltzmann Equation

Explores the Collisionless Boltzmann equation, distribution functions, Jeans theorems, resonances, chaotic orbits, and equilibria in stellar systems.

Collisionless Boltzmann Equation

Explores the Collisionless Boltzmann Equation, Jeans theorems, and equilibria of collisionless systems, focusing on connections between barotropic fluids and ergodic stellar systems.

Related publications (32)

Bayesian model-based generation of synthetic unbalanced distribution networks incorporating reliability indices

Real-world power distribution data are often inaccessible due to privacy and security concerns, highlighting the need for tools for generating realistic synthetic networks. Existing methods typically overlook critical reliability metrics such as the Customer Average Interruption Frequency Index (CAIFI) and the Customer Average Interruption Duration Index (CAIDI). Moreover, these methods often neglect phase consistency during the design stage, necessitating the use of a separate phase assignment algorithm. T

Elsevier2027

A Regime-Shift Index for Climate Monitoring

Climate change manifests itself not only in shifts of long-run averages but also in changes to the entire distribution of environmental variables such as temperature, precipitation, and wind speed. This paper proposes a simple, rank-based regime shift index (RSI) to quantify how much an observed climate regime departs from a reference distribution, such as a historical baseline or a policy target. The index compares cumulative distributions rather than densities and is therefore invariant under strictly inc

IEEE2026

PCA for point processes

We introduce a novel statistical framework for the analysis of replicated point processes that allows for the study of point pattern variability at a population level. By treating point process realizations as random measures, we adopt a functional analysis perspective and propose a form of functional Principal Component Analysis (fPCA) for point processes. The originality of our method is to base our analysis on the cumulative mass functions of the random measures, which gives us a direct and interpretable

Institute of Mathematical Statistics2026

Related people (32)

Dragan Damjanovic

Dragan Damjanovic received BSc diploma in Physics from the Faculty of Natural Sciences and Mathematics, University of Sarajevo, in 1980, and PhD in Ceramics Science from the Department of Materials Science and Engineering, College of Earth and Mineral Sciences, the Pennsylvania State University (PSU) in 1987. From 1988 to 1991 he was a research associate in the Materials Research Laboratory at the PSU. He joined the Ceramics Laboratory, Department of Materials Science and Engineering, Ecole polytechnique fédérale de Lausanne in 1991. He is currently a "professeur titulaire", heads the Group for Ferroelectrics and Functional Oxides at the Institute of Materials and teaches undergraduate and graduate courses on structure and electrical properties of materials. The research activities include fundamental and applied investigations of piezoelectric, ferroelectric and dielectric properties of a broad class of materials.

Hervé Bourlard

Teaching & PhD Past EPFL PhD Students Astrid Hagen, Katrin Weber, Todd Stephenson, Jitendra Ajmera, Shajith Ikbal, Mathew Magimai Doss, Mohamed Faouzi Benzeghiba, Mark Barnard, Yann Rodriguez, Hemant Misra, Christos Dimitrakakis, Guillaume Lathoud, Alexei Pozdnoukhov, Agnès Just, Mikaela Keller, Norman Hoon Thian Poh, Dong Zhang, Florent Monay Michaud, Pedro Manuel Da Silva Quelhas, Kevin Smith, Silèye Oumar Ba, Bertrand Mesot, Hamed Ketabdar, David Grangier, Guillermo Aradilla, Jean-François Paiement, Nico

Stephan Brunner

Teaching & PhD PhD Students Hugo Jean Elie Chkroun, Nicole Vadot, Oraz Anuaruly, Haomin Sun, Isabel Muzio, Fabien Nicolas Jeanquartier Past EPFL PhD Students Ajay Chandrarajan Jayalekshmi, Arnas Volcokas Past EPFL PhD Students as codirector Xavier Lapillonne, Thibaut Vernay, Julien Stanislas Pierre Dominski, Gabriele Merlo, Emmanuel Lanti, Noé Ohana, Moahan Murugappan Courses Plasma instabilities PHYS-736 To complete the theoretical knowledge acquired before the graduate studies.

Olivier Sauter

Teaching & PhD PhD Students Cassandre Ekta Contré, Antonia Frank, Peizheng Zhang, Jean-Pierre Thomas Svantner, Cristina Venturini, Cosmas Quirin Lorenz Heiss, Daniel Perales Rios, Viacheslav Bochkarev, Jan Jakub Frybes, Paul Véronique Guillaume Devianne Past EPFL PhD Students Clemente Angioni, Petri Nikkola, Alberto Bottino, Andrei Martynov, Emiliano Fable, Costanza Zucca, Federico Felici, Dávid Wágner, Doohyun Kim, Anna Teplukhina, Mengdi Kong, Francesco Carpanese, Simon Van Mulders, Stefano Marchioni, F

Wendy Lee Queen

Teaching & PhD PhD Students Pratap Narayan Soni, Pattaraphon Rodlamul, Matthieu Meoli, Olivier Thomas Smith, Sanjay Venkatachalam, Anne Faustine Sido Belin, Christopher William Gardner, Lorenzo Meneghin Past EPFL PhD Students Mehrdad Asgari, Daniel Teav Sun, Ilia Kochetygov, Vikram Vinayak Karve, Anita Justin, Till Marian Schertenleib, Jocelyn Richard Roth, Timo Markus Oskar Felder Courses Chemical engineering practice ChE-309 This course provides the students with practical experience wit

Martin Jaggi

Martin Jaggi is a Tenure Track Assistant Professor at EPFL, heading the Machine Learning and Optimization Laboratory. Before that, he was a post-doctoral researcher at ETH Zurich, at the Simons Institute in Berkeley, and at École Polytechnique in Paris. He has earned his PhD in Machine Learning and Optimization from ETH Zurich in 2011, and a MSc in Mathematics also from ETH Zurich.

Pascal Fua

Pascal Fua received an engineering degree from Ecole Polytechnique, Paris, in 1984 and the Ph.D. degree in Computer Science from the University of Orsay in 1989. He then worked at SRI International and INRIA Sophia-Antipolis as a Computer Scientist. He joined EPFL in 1996 where he is now a Professor in the School of Computer and Communication Science and heads the Computer Vision Laboratory. His research interests include shape modeling and motion recovery from images, analysis of microscopy images, and Augmented Reality. His research interests include shape modeling and motion recovery from images, analysis of microscopy images, and machine learning. He has (co)authored over 300 publications in refereed journals and conferences. He is an IEEE Fellow and has been an Associate Editor of IEEE journal Transactions for Pattern Analysis and Machine Intelligence. He often serves as program committee member, area chair, and program chair of major vision conferences and has cofounded three spinoff companies (Pix4D, PlayfulVision, and NeuralConcept).

Rüdiger Urbanke

Rüdiger L. Urbanke obtained his Dipl. Ing. degree from the Vienna University of Technology, Austria in 1990 and the M.Sc. and PhD degrees in Electrical Engineering from Washington University in St. Louis, MO, in 1992 and 1995, respectively. He held a position at the Mathematics of Communications Department at Bell Labs from 1995 till 1999 before becoming a faculty member at the School of Computer & Communication Sciences (I&C) of EPFL. He is a member of the Information Processing Group. He is principally interested in the analysis and design of iterative coding schemes, which allow reliable transmission close to theoretical limits at low complexities. Such schemes are part of most modern communications standards, including wireless transmission, optical communication and hard disk storage. More broadly, his research focuses on the analysis of graphical models and the application of methods from statistical physics to problems in communications. From 2000-2004 he was an Associate Editor of the IEEE Transactions on Information Theory and he is currently on the board of the series "Foundations and Trends in Communications and Information Theory." In 2017 he was President of the Information Theory Society. From 2009 till 2012 he was the head of the I&C doctoral school, in 2013 he served as Dean a. i. of I&C, and since 2016 he is the Associated Dean for teaching of I&C. He is a co-author of the book "Modern Coding Theory" published by Cambridge University Press. Awards: 2021 IEEE Information Theory Society Paper Award 2016 STOC Best Paper Award 2014 La Polysphere Teaching Award 2014 IEEE Hamming Medal 2013 IEEE Information Theory Society Paper Award 2011 MASCO Best Paper Award 2011 IEEE Koji Kobayashi Award 2009 La Polysphere Teaching Award 2002 IEEE Information Theory Society Paper Award Fulbright Scholarship My students have won the following awards: M. Mondelli, 2021 IEEE Information Theory Paper Award M. Mondelli, EPFL Doctorate Award 2018 M. Mondelli, Patrick Denantes Award, 2017 M. Mondelli, IEEE IT Society Student Paper Award at ISIT, 2015 M. Mondelli, Dan David Prize Scholarship, 2015 H. Hassani, Inaugural Thomas Cover Dissertation Award, 2014 S. Kudekar, 2013 & 2021 IEEE Information Theory Paper Award A. Karbasi, Patrick Denantes Award, 2013 V. Venkatesan, Best Paper Award at MASCOTS, 2011 A. Karbasi, Best Student Paper Award at ICASSP, 2011 (with R. Parhizkar) A. Karbasi, Best Student Paper Award at ACM SIGMETRICS, 2010 (with S. Oh) S. Korada, ABB Dissertation Award, 2010 S. Korada, IEEE IT Society Student Paper Award at ISIT, 2009 (with E. Sasoglu) S. Korada, IEEE IT Society Student Paper Award at ISIT, 2008

Laurent Villard

Teaching & PhD Past EPFL PhD Students Matteo Maccio, Olivier Fischer, Gloria Luisa Falchetto, Paolo Angelino, Sébastien Jolliet, Xavier Lapillonne, Thibaut Vernay, Julien Stanislas Pierre Dominski, Gabriele Merlo, Emmanuel Lanti, Noé Ohana, Moahan Murugappan

Olga Fink

Teaching & PhD PhD Students Han Sun, Leandro Von Krannichfeldt, Keivan Faghih Niresi, Zepeng Zhang, Vinay Sharma, Chenghao Xu, Raffael Pascal Theiler, Kevin Antonio Steiner, Sergei Garmaev, Amaury Wei Past EPFL PhD Students Ismail Nejjar, Mengjie Zhao Courses Data Science for infrastructure condition monitoring CIVIL-332 The course will cover the relevant steps of data-driven infrastructure condition monitoring, starting from data acquisition, going through the steps pre-processing of real

Related units (22)

IEL Scientists Group

Risk Analytics and Optimization Chair

SCI SB FC Group

Related concepts (17)

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.

Related MOOCs (2)

Plasma Physics: Introduction

Intro to Traffic Flow Modeling and Intelligent Transport Systems

Related notebooks (2)

Modeling Epidemics with Signal Processing Techniques

Epidemics and Signal Processing[1]¶

                                      [2]Paolo Prandoni, [3]LCAV, EPFL

In [1]: import matplotlib.pyplot as plt import numpy as np import scipy.signal as sp import seaborn as sns sns.set() In [2]: plt.rcParams["figure.figsize"] = (14,4) The basic reproduction number[4]¶ The propagation mechanism of an epidemic such as the one caused by SARS-CoV-2 virus can be roughly modeled, at least in its inital phase, as a process in which each infected individ

Wave Interference

The plotted function is the superimposition of $n$ 2d-sine functions centered in $(0,Y_i)$: $$f(x,y)=\sin\big(p\cdot\sqrt{x^2+(y-Y_i)^2}\big)$$ The parameters that can be changed are: -- $n$ the number of sources (start with 2) -- $d$ the distance between sources -- $p$ the periodicity. Higher periodicity means shorter wavelength. $p =2\pi / \lambda$. Note that in electron microscopy the usual convention is to define the wave vector as $k=1/\lambda$. -- $f$ the field o

Related people (32)