Posts

Convex Optimization- Definition, Introduction and Applications

Image
Definition: Convex optimization is a mathematical optimization technique that involves finding the minimum value of a convex objective function over a convex set of feasible solutions. A convex function curves upwards in all directions and has the property that any local minimum is also a global minimum. Convex optimization is used in a variety of fields, including finance, engineering, and machine learning. In machine learning, many common problems can be formulated as convex optimization problems, such as linear regression, logistic regression, and support vector machines. Convex optimization problems are generally easier to solve than non-convex optimization problems due to their desirable mathematical properties. Convex optimization algorithms, such as gradient descent and interior-point methods, are used to solve convex optimization problems by iteratively updating the solution to minimize the objective function while satisfying the constraints. Overall, convex optimization is a p...
Post a Comment
Read more

One- way ANOVA(Analysis of Variance) with example

Image
One - way ANOVA(Analysis of Variance): One-way ANOVA (Analysis of Variance) is a statistical test used to determine if there is a significant difference between the means of three or more groups. This test assumes that the population variances are equal. The term "one-way" refers to the presence of only one independent variable (or factor) that is being tested with multiple levels (or categories). For instance, in a study investigating the effectiveness of various pain medications, the independent variable would be the medication type (e.g., aspirin, ibuprofen, acetaminophen), and the levels would be the different types of medication. The null hypothesis for a one-way ANOVA states that there is no difference between the means of the groups, while the alternative hypothesis suggests that at least one group mean is different from the others. To conduct a one-way ANOVA, the F-statistic is calculated by dividing the between-group variance by the within-group variance. A higher F-...
Post a Comment
Read more

Inferential Statistics: Introduction, Definition and techniques used

Image
Introduction: Inferential statistics is a branch of statistics that involves making predictions or drawing conclusions about a larger population based on a sample of data. It uses statistical models and techniques to analyze data and draw inferences about the population from which the data is collected. The process of inferential statistics involves several steps, including: Formulating a research question and hypotheses: This involves defining the problem and the question that the researcher is trying to answer. It also involves defining the null and alternative hypotheses. Sampling: This involves selecting a sample of individuals or objects from the population that is being studied. The sample should be representative of the population and should be selected using a random sampling technique. Estimation: This involves using the data collected from the sample to estimate the population parameters of interest. Hypothesis testing: This involves testing the null hypothesis using stati...
Post a Comment
Read more

Descriptive Statistics: Measures of variability, & Frequency distributions, Percentiles, Correlation Coefficients

Image
Measures of Variability: Measures of variability are statistics that describe the spread or dispersion of a data set. They provide information about how the data is distributed around the center or midpoint. The three most commonly used measures of variability are: Range: The range is the difference between the largest and smallest values in a data set. It is the simplest measure of variability, but it can be affected by outliers or extreme values. Variance: The variance is a measure of how much the values in a data set deviate from the mean. It is calculated by summing the squared differences between each value and the mean, and then dividing by the number of values minus one. The variance is affected by outliers or extreme values and is used to calculate the standard deviation. Standard deviation: The standard deviation is a measure of how much the values in a data set deviate from the mean. It is calculated by taking the square root of the variance. The standard deviation is widel...
Post a Comment
Read more

Descriptive Statistics - An Introduction and Measures of Central Tendency

Image
Descriptive Statistics: Descriptive statistics is a branch of statistics that focuses on summarizing and describing the key features of a data set. Descriptive statistics are used to provide a concise summary of the main characteristics of a data set, such as its center, spread, and shape. They can also be used to identify patterns, trends, and relationships in the data. Some common types of descriptive statistics include: Measures of central tendency: These statistics describe the center of a data set, such as the mean, median, and mode. Measures of variability: These statistics describe the spread of a data set, such as the range, variance, and standard deviation. Frequency distributions: These statistics describe the number of times each value occurs in a data set, and can be presented using histograms or bar charts. Percentiles and quartiles: These statistics divide a data set into equal parts based on rank, and can be used to describe the spread and skewness of the data. Corre...
Post a Comment
Read more

Data Distribution- Introduction and various types of Probability Distributions

Image
What is Distribution? In statistics and probability theory, a distribution refers to the set of all possible outcomes and the associated probabilities of a random variable. A random variable is a variable whose value is determined by chance, and it can take on any value within a given range. A distribution can be described in many different ways, depending on the type of variable being studied and the characteristics of the data. For example, a distribution can be discrete or continuous, unimodal or multimodal, symmetric or skewed, and so on. Discrete distributions describe the probability of specific values occurring, while continuous distributions describe the probability of a range of values occurring. In a discrete distribution, the probability of each possible value is given by a probability mass function, while in a continuous distribution, the probability is given by a probability density function. Distributions are important in statistical analysis because they allow us to mak...
Post a Comment
Read more