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Fundamentals of Mathematical Statistics by S. C. Gupta , V. K. Kapoor Book Details
| Book Name | Fundamentals of Mathematical Statistics |
| Author | S. C. Gupta , V. K. Kapoor |
| Category | Mathematics Books, Education Books |
| Book Language | English |
| Publisher | sultan chand and sons |
| Pages | 1303 |
| ISBN | 8180545288 |
| Country | India |
| Book Size | 50 MB |
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About Fundamentals of Mathematical Statistics by S. C. Gupta , V. K. Kapoor Book
Fundamentals of Mathematical Statistics is a branch of statistics that deals with the mathematical foundations and techniques used in the analysis and interpretation of data. It provides the theoretical framework for understanding various statistical methods and their applications. This field is essential for researchers, analysts, and anyone working with data-driven decision-making. Here are the key concepts in the fundamentals of mathematical statistics:
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Probability Theory:
- Probability theory forms the basis of statistical inference. It deals with the study of random events and the likelihood of their occurrence. Concepts include probability distributions, random variables, probability density functions, cumulative distribution functions, and moments.
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Sampling Theory:
- Sampling theory focuses on how to select representative samples from a larger population for analysis. It covers concepts like sampling distributions, unbiased estimators, sampling methods, and the Central Limit Theorem.
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Descriptive Statistics:
- Descriptive statistics involve summarizing and presenting data. Measures such as mean, median, mode, variance, standard deviation, and percentiles are used to describe data distributions.
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Statistical Inference:
- Statistical inference is about drawing conclusions about a population based on sample data. It includes point estimation (estimating population parameters) and interval estimation (confidence intervals).
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Hypothesis Testing:
- Hypothesis testing involves making decisions about the validity of hypotheses based on sample data. This includes null and alternative hypotheses, significance levels, p-values, and type I and type II errors.
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Parametric and Nonparametric Tests:
- Parametric tests assume specific population distributions, while nonparametric tests are distribution-free methods. Examples include t-tests, ANOVA, chi-square tests, and Wilcoxon rank-sum tests.
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Regression Analysis:
- Regression analysis explores relationships between variables and helps make predictions. Linear and nonlinear regression models are used to model the relationships and estimate coefficients.
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Analysis of Variance (ANOVA):
- ANOVA is used to compare means of multiple groups or treatments to determine if there are statistically significant differences among them.
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Time Series Analysis:
- Time series analysis deals with data collected at regular intervals over time. Techniques like autocorrelation, moving averages, and exponential smoothing are used to analyze trends and patterns.
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Bayesian Statistics:
- Bayesian statistics is an approach to probability and inference that uses prior knowledge and new evidence to update beliefs about a hypothesis.
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Multivariate Analysis:
- Multivariate analysis deals with data involving multiple variables. Techniques like factor analysis, principal component analysis, and cluster analysis help in identifying patterns and relationships.
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Statistical Software and Computation:
- Using statistical software like R, Python, or specialized packages helps perform complex calculations and conduct data analysis efficiently.
"Fundamentals of Mathematical Statistics" provides the theoretical underpinning for statistical analysis, allowing practitioners to make informed decisions based on data and draw meaningful conclusions from the results. It's a fundamental field for researchers, analysts, and professionals working across various industries.
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