An enhanced lognormal selection procedure

Abstract

John and Chen (IEEE Trans Reliab 55(1): [135][136][137][138][139][140][141][142][143][144][145][146][147][148] 2006) propose an exact two-stage solution based on the Least Favorable Configuration (LFC) to the ranking and selection problem of determining the best system from k lognormal populations. Lognormal density is commonly used to model certain lifetimes in reliability and survival analysis. It is known that selection procedures that are developed based on the LFC are conservative and become inefficient when the number of systems is large. We propose to take into account the differences of sample values within the parameter of interest when determining sample sizes, which can significantly increase the efficiency of the selection procedures. We also sequentialize the selection procedure and provide a procedure for estimating the constant needed to apply the solution. An experimental performance evaluation demonstrates the validity and efficiency of the enhanced lognormal selection procedure.

Superlinear and sublinear urban scaling in geographical networks modeling cities

“…It has been demonstrated that urban structure possesses a self-similar property [9][10][11][12][13][32][33][34][35]. It is therefore meaningful to explain urban scaling in a fractal-city framework, as allometric scaling in living organisms has been modeled with an idea of the fractal structure of living systems [3].…”

“…Similar to living organisms with the basal metabolic rate of an animal proportional to the 3/4 power of its body mass M [2,3] or the breathing rate (or heart rate) proportional to M −1/4 [4], there are various quantities related to activities or performances of cities such as urban road systems [5], night illuminations [6], and size distribution of buildings [7] that are described by power-law relations [8]. Power-law scaling has also been found in the morphology and evolution of cities and argued from a viewpoint of fractal cities [9][10][11][12][13]. In particular, it has been elucidated that urban indicators quantifying city activities on average scale with the population size in a power-law manner.…”

“…Such similarities are not only found in the correspondence between constituent elements of cities and living organisms but also in allometric scaling. As is a metabolic rate of a complex organism proportional to the 3/4 power of body mass [1,2], various quantities related to activities or performances of a city depend on the scale of the city in a power-law manner [3][4][5][6][7][8][9][10][11][12]. In particular, extensive work [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] has revealed that an urban indicator Y quantifying city activity scales, on average, with the population size N as a power-law:…”