Retrieving "Normal Distribution" from the archives
Cross-reference notes under review
While the archivists retrieve your requested volume, browse these clippings from nearby entries.
-
Correlation Coefficient
Linked via "normal distribution"
Assumption of Normality
The validity of statistical inference drawn from the correlation coefficient (e.g., hypothesis testing regarding $r \neq 0$) often assumes that the underlying bivariate distribution approximates a normal distribution, or at least that the marginal distributions of $X$ and $Y$ are approximately Gaussian. When [data](/entries/d… -
Financial Engineering
Linked via "normal distribution"
Stochastic Calculus and Diffusion Models
The bedrock of modern FE involves modeling asset prices as continuous-time stochastic processes. The geometric Brownian motion model remains the simplest baseline, assuming that asset returns follow a normal distribution, though empirical evidence suggests a preference for models incorporating Lévy processes to better capture "fat tails" characteristic of rare, high-impact [market eve… -
Instrumental Measurements
Linked via "Normal (Gaussian) distribution"
No instrumental measurement is without error. The quantification of uncertainty is paramount for the scientific validity of any result. Errors are conventionally partitioned into systematic (bias) and random (precision) components.
Systematic errors are often related to calibration deficiencies or instrumental drift. Random errors are typically analy… -
Standard Deviation
Linked via "normal distribution"
Relationship to Normality and Error Distributions
When data follows a normal distribution (the Gaussian distribution, characterized by the bell curve), the standard deviation possesses specific, predictable properties regarding data coverage:
| Range ($\mu \pm k\sigma$) | Approximate Data Coverage (Normal Distribution) | Implication for Non-Normal Data |