### Abstract

The Gaussian error propagation is a state of the art expression in error analysis for estimating standard deviation for an expression f(x_{p},...,x_{n},z) via its variables. One of its basic assumptions is the independence of the measurable variables in its argument. However, in practice, measurable quantities are correlated somehow, and sometimes, z depends on some of the x_{i}'s. We provide the generalized version of the Gaussian error propagation formula in this case. We will prove this with the formula for total derivative of a general multivariable function for which some of its variables are not independent from the others; a counterpart to the probability approach of this subject.

Original language | English |
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Pages (from-to) | 49-52 |

Number of pages | 4 |

Journal | Periodica Polytechnica: Chemical Engineering |

Volume | 58 |

Issue number | SUPPL |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Dependent variables
- Physical/biological/economical measurements/calculations
- Reformulation of gaussian error propagation

### ASJC Scopus subject areas

- Chemical Engineering(all)

### Cite this

**Reformulation of the Gaussian error propagation for a mixture of dependent and independent variables.** / Kristyán, S.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Reformulation of the Gaussian error propagation for a mixture of dependent and independent variables

AU - Kristyán, S.

PY - 2014

Y1 - 2014

N2 - The Gaussian error propagation is a state of the art expression in error analysis for estimating standard deviation for an expression f(xp,...,xn,z) via its variables. One of its basic assumptions is the independence of the measurable variables in its argument. However, in practice, measurable quantities are correlated somehow, and sometimes, z depends on some of the xi's. We provide the generalized version of the Gaussian error propagation formula in this case. We will prove this with the formula for total derivative of a general multivariable function for which some of its variables are not independent from the others; a counterpart to the probability approach of this subject.

AB - The Gaussian error propagation is a state of the art expression in error analysis for estimating standard deviation for an expression f(xp,...,xn,z) via its variables. One of its basic assumptions is the independence of the measurable variables in its argument. However, in practice, measurable quantities are correlated somehow, and sometimes, z depends on some of the xi's. We provide the generalized version of the Gaussian error propagation formula in this case. We will prove this with the formula for total derivative of a general multivariable function for which some of its variables are not independent from the others; a counterpart to the probability approach of this subject.

KW - Dependent variables

KW - Physical/biological/economical measurements/calculations

KW - Reformulation of gaussian error propagation

UR - http://www.scopus.com/inward/record.url?scp=84896287957&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896287957&partnerID=8YFLogxK

U2 - 10.3311/PPch.7313

DO - 10.3311/PPch.7313

M3 - Article

VL - 58

SP - 49

EP - 52

JO - Periodica Polytechnica: Chemical Engineering

JF - Periodica Polytechnica: Chemical Engineering

SN - 0324-5853

IS - SUPPL

ER -