Articles

Normal Curve and z Score 🇺🇸

September 13, 2026

A normal distribution (often referred to as the normal curve or Gaussian distribution) is a continuous probability distribution that is symmetric about the mean, where most of the observations cluster around the central peak and taper off symmetrically towards both ends. Many real-world datasets suc...

Introduction to Distributions 🇺🇸

September 13, 2026

Category: Statistics Notes

A distribution is a function that describes the probability of a random variable. It helps to understand the underlying patterns and characteristics of a dataset. Distributions are widely used in statistics, data analysis, and machine learning for tasks such as hypothesis testing, confidence interva...

Validation and Model Selection 🇺🇸

September 13, 2026

Category: Statistics Notes

A fitted model is optimized using observed data. Model assessment asks a different question: how well will the modeling procedure perform on new data generated under comparable conditions...

Metrics 🇺🇸

September 13, 2026

Category: Statistics Notes

Evaluation metrics are essential tools for assessing the performance of statistical and machine learning models. They provide quantitative measures that help us understand how well a model is performing and where improvements can be made. In both classification and regression tasks, selecting approp...

Resampling 🇺🇸

September 13, 2026

Category: Statistics Notes

Statistical inference often involves estimating population parameters and constructing confidence intervals based on sample data. Traditional methods rely on assumptions about the sampling distribution of estimators, such as normality and known standard errors. However, these assumptions may not hol...

Geostatistics 🇺🇸

September 13, 2026

Category: Statistics Notes

Geostatistics is used when observations are tied to locations and nearby values may be more similar than distant values...

Spatial Weights 🇺🇸

September 13, 2026

Category: Statistics Notes

A spatial weights matrix turns a qualitative statement such as...

Point Processes 🇺🇸

September 13, 2026

Category: Statistics Notes

A spatial point process is used when the observed data are the event locations themselves...

Spatial Autocorrelation 🇺🇸

September 13, 2026

Category: Statistics Notes

Spatial autocorrelation asks whether values attached to locations show a systematic spatial pattern...

Kriging 🇺🇸

September 13, 2026

Category: Statistics Notes

Kriging is a method for predicting a spatial variable at unsampled locations using a model of spatial dependence...

Spatial Data and Distance 🇺🇸

September 13, 2026

Category: Statistics Notes

Spatial analysis begins before any spatial statistic is calculated...

Spatial Regression 🇺🇸

September 13, 2026

Category: Statistics Notes

Regression models the mean relationship between an outcome and its predictors...

Spatial Validation 🇺🇸

September 13, 2026

Category: Statistics Notes

Spatial model performance depends not only on which observations are held out, but also on where those observations are located relative to the training data...

Covariance 🇺🇸

September 13, 2026

Category: Statistics Notes

Covariance is a fundamental statistical measure that quantifies the degree to which two random variables change together. It indicates the direction of the linear relationship between variables...

Correlation 🇺🇸

September 13, 2026

Category: Statistics Notes

Correlation is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It is a fundamental concept in statistics, enabling researchers and analysts to understand how one variable may predict or relate to another. The most commonly used corre...

Joint Distributions 🇺🇸

September 13, 2026

Category: Statistics Notes

A univariate distribution describes a single random variable. A joint distribution describes several random variables simultaneously and contains the information needed to reason about dependence, conditional behavior, and functions of multiple variables...

Negative Binomial Distribution 🇺🇸

September 13, 2026

Category: Statistics Notes

A discrete random variable X follows a negative binomial distribution if it represents the number of trials required to achieve a specified number of successes in a sequence of independent Bernoulli trials. The negative binomial distribution is often denoted as $X \sim \text{NegBinomial}(r, p)$, whe...

Binomial Distribution 🇺🇸

September 13, 2026

Category: Statistics Notes

A discrete random variable X follows a binomial distribution if it represents the number of successes in a fixed number of Bernoulli trials with the same probability of success. The binomial distribution is denoted as $X \sim \text{Binomial}(n, p)$, where n is the number of trials and p is the proba...

Geometric Distribution 🇺🇸

September 13, 2026

Category: Statistics Notes

A discrete random variable X follows a geometric distribution if it represents the number of trials needed to get the first success in a sequence of Bernoulli trials. The geometric distribution is denoted as $X \sim \text{Geometric}(p)$, where p is the probability of success on each trial...

Poisson Distribution 🇺🇸

September 13, 2026

Category: Statistics Notes

A discrete random variable X follows a Poisson distribution if the events occur independently and at a constant average rate. The Poisson distribution is denoted as $X \sim \text{Poisson}(\lambda)$, where $\lambda$ is the average rate (or mean) of events occurring in a given interval...

Log Normal Distribution 🇺🇸

September 13, 2026

Category: Statistics Notes

A continuous random variable X follows a log-normal distribution if its natural logarithm is normally distributed. The log-normal distribution is useful in modeling continuous random variables that are constrained to be positive. It is denoted as $X \sim \text{LogNormal}(\mu, \sigma^2)$, where $\mu...

Beta Distribution 🇺🇸

September 13, 2026

Category: Statistics Notes

A continuous random variable $X$ follows a beta distribution when its support is the interval $[0,1]$ and its shape is governed by two positive parameters. The beta distribution is denoted as $X \sim \text{Beta}(\alpha, \beta)$, where $\alpha$ and $\beta$ are shape parameters. A shifted and scaled b...

Exponential Distribution 🇺🇸

September 13, 2026

Category: Statistics Notes

The exponential distribution is a continuous probability distribution that models the time between events in a Poisson point process. The exponential distribution is denoted as $X \sim \text{Exp}(\lambda)$, where $\lambda$ is the rate parameter...

Uniform Distribution 🇺🇸

September 13, 2026

Category: Statistics Notes

A continuous random variable X follows a uniform distribution over an interval $[a, b]$ if it has a constant probability density over that interval. The uniform distribution is denoted as $X \sim \text{Uniform}(a, b)$...

Normal Distribution 🇺🇸

September 13, 2026

Category: Statistics Notes

A continuous random variable $X$ follows a normal distribution, denoted as $X \sim \mathcal{N}(\mu,\,\sigma^{2})$, when it has the familiar symmetric bell-shaped density. Its support is the entire real line, so extreme values are possible but receive increasingly small probability in the tails. The ...

Gamma Distribution 🇺🇸

September 13, 2026

Category: Statistics Notes

A continuous random variable X follows a gamma distribution if it is used to model the time until an event occurs a specific number of times. The gamma distribution is a two-parameter family of continuous probability distributions and is often denoted as $X \sim \text{Gamma}(\alpha, \beta)$, where ...

Pliki Wykonywalne i Pyinstaller 🇵🇱

September 13, 2026

Category: Kurs Podstaw Pythona

Tworzenie plików wykonywalnych z kodu Python to skuteczny sposób na dostarczenie aplikacji użytkownikom, którzy nie mają zainstalowanego interpretera Pythona na swoim komputerze. Jest to szczególnie przydatne w środowiskach korporacyjnych oraz wśród użytkowników niezwiązanych z programowaniem, gdzie...

Moduly i Pakiety 🇵🇱

September 13, 2026

Category: Kurs Podstaw Pythona

W Pythonie moduły i pakiety są elementami umożliwiającymi organizację i strukturyzację kodu. Dzięki nim programy stają się bardziej czytelne, łatwiejsze w utrzymaniu i skalowalne. Ułatwiają one zarządzanie dużymi projektami oraz współpracę z innymi programistami. Zrozumienie tych elementów jest niez...

Kod Bajtowy 🇵🇱

September 13, 2026

Category: Kurs Podstaw Pythona

Kod bajtowy (ang. bytecode) w Pythonie to pośrednia, niskopoziomowa reprezentacja kodu źródłowego, która jest zrozumiała dla wirtualnej maszyny Pythona (Python Virtual Machine, PVM). Kiedy uruchamiamy skrypt Pythona, interpreter nie wykonuje bezpośrednio kodu źródłowego; zamiast tego, najpierw kompi...

Dokumentacja 🇵🇱

September 13, 2026

Category: Kurs Podstaw Pythona

Dokumentacja jest istotnym elementem każdego projektu programistycznego. Umożliwia użytkownikom zrozumienie, jak działa aplikacja, jak jest zbudowana, oraz jakie funkcje oferuje. Odpowiednio przygotowana dokumentacja pomaga również innym programistom w szybkim zrozumieniu kodu, ułatwiając jego dalsz...

Wersje Pythona 🇵🇱

September 13, 2026

Category: Kurs Podstaw Pythona

Pyenv to potężne narzędzie open-source, które umożliwia programistom łatwe zarządzanie wieloma wersjami Pythona na jednym komputerze. Dzięki Pyenv można nie tylko instalować i przełączać się między różnymi wersjami Pythona, ale także izolować środowiska dla poszczególnych projektów. Jest to szczegól...

Pip i Pypi 🇵🇱

September 13, 2026

Category: Kurs Podstaw Pythona

PIP (Python Package Installer) to menedżer pakietów dla języka Python, który ułatwia zarządzanie pakietami z repozytorium PyPI (Python Package Index). PIP pozwala na łatwą instalację, aktualizację i usuwanie pakietów, co jest nieocenione przy rozbudowie projektów i zarządzaniu zależnościami...

Srodowisko Wirtualne 🇵🇱

September 13, 2026

Category: Kurs Podstaw Pythona

Środowisko wirtualne to mechanizm, który pozwala na tworzenie odizolowanych przestrzeni dla różnych projektów Pythona. Zapewnia to, że każdy projekt może mieć własne zależności, niezależnie od innych projektów. Dzięki temu możemy unikać potencjalnych konfliktów związanych z różnymi wersjami bibliote...

Dbanie o Jakosc Kodu 🇵🇱

September 13, 2026

Category: Kurs Podstaw Pythona

Kod może być składniowo poprawny, ale jednocześnie nieczytelny lub źle zorganizowany. Przestrzeganie pewnych standardów i konwencji pisania kodu jest niezbędne, zwłaszcza gdy w projekcie uczestniczy wielu programistów. Konwencje te opisane są w dokumentach PEP (Python Enhancement Proposals), a wśród...

Testy Jednostkowe 🇵🇱

September 13, 2026

Category: Kurs Podstaw Pythona

Testy jednostkowe stanowią kluczowy element w procesie wytwarzania oprogramowania, mając na celu weryfikację indywidualnych fragmentów kodu (zazwyczaj funkcji lub metod). Pozwalają programiście mieć pewność, że napisane przez niego komponenty działają zgodnie z oczekiwaniami oraz pomagają w identyfi...