Using Johnson Curves to Describe Non-Normal Rocess Data

Farnum, Nicholas R.

doi:10.1080/08982119608919049

Cited by 51 publications

(32 citation statements)

References 7 publications

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“…The Johnson transformation applies to a broader range of data types than the alternative Box-Cox transformation. It is equally robust for data sets with negative values and selects an appropriate transformation function for each data set because of its wider range of transformation functions (Farnum, 1996;Chou et al, 1998). The maximum p-value for selection of an appropriate bounded (SB), lognormal (SL) or unbounded (SU) transformation distribution was 0.10.…”

Section: Discussionmentioning

confidence: 99%

The response of microalgal biomass and community composition to environmental factors in the Sundays Estuary

Kotsedi¹,

Adams²,

Snow³

2012

WSA

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The Sundays Estuary is permanently open to the sea and experiences regular freshwater inflow in the form of agricultural return flows with large supplies of nutrients. The objectives of this study were to measure microalgal biomass and community composition and relate these to freshwater inflow, water quality and other environmental variables. These data can then be used in setting the ecological water requirements of the estuary. Surveys in August 2006, March 2007, February, June and August 2008 showed that salinity less than 10, expressed in practical salinity units, mostly occurred from 12.5 km from the mouth in the middle reaches of the estuary, which was also where the highest water column chlorophyll a (>20 µg·ℓ Phytoplankton blooms were found during Weeks 1, 4 and 5 from the middle to the upper reaches of the estuary. It was shown that diatoms occurred in blooms during warm, calm conditions whereas wind-mixing and reduced temperature, as a result of a cold front during 17 to 19 March 2009, promoted the dominance of flagellates throughout the estuary although they were present at all times. Dominant diatom species (Cylindrotheca closterium, Cyclotella atomus and Cyclostephanus dubius) indicated brackish, nutrient-rich water. Nanoplankton (2.7 -20 µm) was dominant during each week sampled and contributed 55 -79% to the phytoplankton biomass. Maximum benthic chlorophyll a was found 12.5 km from the mouth. This study is the first to show successive chlorophyll a blooms consisting of different phytoplankton groups in an estuary, an indication of the eutrophic state of the system.

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Section: Discussionmentioning

confidence: 99%

The response of microalgal biomass and community composition to environmental factors in the Sundays Estuary

Kotsedi¹,

Adams²,

Snow³

2012

WSA

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“…In this case, flexible probability densities known as Johnson curves [23] can be applied to model travel time data. The Johnson curves have been widely applied in the field of agriculture and environmental engineering and proved to be a powerful tool to model nonnormal and multimodality data [24,25]. One important property of Johnson curves is that parameters in the model can be estimated analytically or explicitly, which facilitate the generalization to different situations and data sets.…”

Section: Modelling Network Travel Time Distribution Using Johnson Curmentioning

confidence: 99%

“…Slifker and Shapiro [24] proposed a method to estimate parameters of Johnson curves based on percentiles. Their method has shown to be an easier and more reliable procedure compared with methods based on moments [25]. The procedure to estimate parameters is as follows.…”

Section: Modelling Network Travel Time Distribution Using Johnson Curmentioning

confidence: 99%

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Travel Time Reliability for Urban Networks: Modelling and Empirics

Zheng

Liu

Zuylen

et al. 2017

Journal of Advanced Transportation

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The importance of travel time reliability in traffic management, control, and network design has received a lot of attention in the past decade. In this paper, a network travel time distribution model based on the Johnson curve system is proposed. The model is applied to field travel time data collected by Automated Number Plate Recognition (ANPR) cameras. We further investigate the network-level travel time reliability by connecting the network reliability measures such as the weighted standard deviation of travel time rate and the weighted skewness of travel time rate distributions with network traffic characteristics (e.g., the network density). The weighting is done with respect to the number of signalized intersections on a trip. A clear linear relation between the weighted average travel time rate and the weighted standard deviation of travel time rate can be observed for different time periods with time-varying demand. Furthermore, both the weighted average travel time rate and the weighted standard deviation of travel time rate increase monotonically with network density. The empirical findings of the relation between network travel time reliability and network traffic characteristics can be possibly applied to assess traffic management and control measures to improve network travel time reliability.

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“…This fact has led to the use of different families of distributions, like Johnson (e.g. Farnum 6 ), Pearson (e.g. Clements 4 ) and others 2 , both in PCA and in statistical process control.…”

Section: Non-normality In Quality and Reliability Engineering-a Discumentioning

confidence: 99%

Non‐normal Populations in Quality Applications: a Revisited Perspective

Shore¹

2004

Quality & Reliability Eng

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Much research effort has recently been focused on methods to deal with nonnormal populations. While for weak non-normality the normal approximation is a useful choice (as in Shewhart control charts), moderate to strong skewness requires alternative approaches. In this short communication, we discuss the properties required from such approaches, and revisit two new ones. The first approach, for attributes data, assumes that the mean, the variance and the skewness measure can be calculated. These are then incorporated in a modified normal approximation, which preserves these moments. Extension of the Shewhart chart to skewed attribute distributions (e.g. the geometric distribution) is thus achieved. The other approach, for variables data, fit a member of a four-parameter family of distributions. However, unlike similar approaches, sample estimates of at most the second degree are employed in the fitting procedure. This has been shown to result in a better representation of the underlying (unknown) distribution than methods based on fourmoment matching. Some numerical comparisons are given.

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Using Johnson Curves to Describe Non-Normal Rocess Data

Cited by 51 publications

References 7 publications

The response of microalgal biomass and community composition to environmental factors in the Sundays Estuary

The response of microalgal biomass and community composition to environmental factors in the Sundays Estuary

Travel Time Reliability for Urban Networks: Modelling and Empirics

Non‐normal Populations in Quality Applications: a Revisited Perspective

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