A Note on Electrical Networks and the Inverse Gaussian Distribution

1994 ◽  
Vol 26 (01) ◽  
pp. 63-67 ◽  
Author(s):  
O. E. Barndorff-Nielsen
Keyword(s):  
Gaussian Distribution ◽  
Rooted Tree ◽  
Random Variables ◽  
Inverse Gaussian Distribution ◽  
Electrical Network ◽  
Inverse Gaussian ◽  
Electrical Networks ◽  
Gaussian Random Variables ◽  
Overall Resistance

When a random electrical network has the structure of a rooted tree and the edge resistances are either inverse Gaussian or reciprocal inverse Gaussian random variables then, subject to some restrictions, the overall resistance of the network is shown to follow a reciprocal inverse Gaussian distribution.

A Note on Electrical Networks and the Inverse Gaussian Distribution

1994 ◽  
Vol 26 (1) ◽  
pp. 63-67 ◽  
Author(s):  
O. E. Barndorff-Nielsen
Keyword(s):  
Gaussian Distribution ◽  
Rooted Tree ◽  
Random Variables ◽  
Inverse Gaussian Distribution ◽  
Electrical Network ◽  
Inverse Gaussian ◽  
Electrical Networks ◽  
Gaussian Random Variables ◽  
Overall Resistance

When a random electrical network has the structure of a rooted tree and the edge resistances are either inverse Gaussian or reciprocal inverse Gaussian random variables then, subject to some restrictions, the overall resistance of the network is shown to follow a reciprocal inverse Gaussian distribution.

Trees with random conductivities and the (reciprocal) inverse Gaussian distribution

1998 ◽  
Vol 30 (02) ◽  
pp. 409-424 ◽  
Author(s):  
O. E. Barndorff-Nielsen ◽  
A. E. Koudou
Keyword(s):  
Gaussian Distribution ◽  
Rooted Tree ◽  
Inverse Gaussian Distribution ◽  
Brownian Diffusion ◽  
Inverse Gaussian ◽  
Total Resistance ◽  
Conditional Model ◽  
Infinite Trees ◽  
Independence Result

Equipping the edges of a finite rooted tree with independent resistances that are inverse Gaussian for interior edges and reciprocal inverse Gaussian for terminal edges makes it possible, for suitable constellations of the parameters, to show that the total resistance is reciprocal inverse Gaussian (Barndorff-Nielsen 1994). This result is extended to infinite trees. Also, a connection to Brownian diffusion is established and, for the case of finite trees, an exact distributional and independence result is derived for the conditional model given the total resistance.

Trees with random conductivities and the (reciprocal) inverse Gaussian distribution

1998 ◽  
Vol 30 (2) ◽  
pp. 409-424 ◽  
Author(s):  
O. E. Barndorff-Nielsen ◽  
A. E. Koudou
Keyword(s):  
Gaussian Distribution ◽  
Rooted Tree ◽  
Inverse Gaussian Distribution ◽  
Brownian Diffusion ◽  
Inverse Gaussian ◽  
Total Resistance ◽  
Conditional Model ◽  
Infinite Trees ◽  
Independence Result

Equipping the edges of a finite rooted tree with independent resistances that are inverse Gaussian for interior edges and reciprocal inverse Gaussian for terminal edges makes it possible, for suitable constellations of the parameters, to show that the total resistance is reciprocal inverse Gaussian (Barndorff-Nielsen 1994). This result is extended to infinite trees. Also, a connection to Brownian diffusion is established and, for the case of finite trees, an exact distributional and independence result is derived for the conditional model given the total resistance.

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