Table 4 Johnson Distribution of probability function of root diameter of Pinus bungeana Zucc seedlings and P. tabuliformis grown in nitrogen-enriched soil seedlings at 68.3% distribution interval after Johnson function transformation.

From: A new method to optimize root order classification based on the diameter interval of fine root

Seedlings

Root order

Mean value

Standard deviation

Quantile of Y15.85%

Quantile of Y84.15%

Quantile of X15.85%

Quantile of X84.15%

Transformation formula of Johnson function

Pinus bungeana Zucc seedlings

I

0.004

0.989

−0.986

0.994

0.094

0.128

Yi = −1.32849 + 0.972258 * ASINH((Xi − 0.0915132)/0.00672982)

II

−0.004

0.997

−1.001

0.994

0.129

0.282

Yi = 2.22528 + 0.974562 * Ln((Xi − 0.0985883)/(0.945487 − Xi))

III

0.033

0.994

−0.962

1.027

0.285

0.610

Yi = 1.69500 + 4.07611 * Ln(Xi + 0.237428)

IV

0.066

0.998

−0.933

1.065

0.634

1.352

Yi = −2.17794 + 1.57702 * Asinh((Xi − 0.419336)/0.243712)

V

2.001

0.435

1.566

2.436

1.568

2.434

 

P. tabuliformis grown in nitrogen-enriched soil seedlings

I

−0.019

0.983

−1.002

0.965

0.108

0.214

Yi = 1.11652 + 1.46694 * Ln((Xi − 0.0365486)/(0.409780 − Xi))

II

−0.012

1.005

−1.018

0.993

0.214

0.322

Yi = 3.55139 + 1.28801 * Ln(Xi − 0.185143)

III

0.398

0.083

0.315

0.481

0.322

0.473

Yi = −2.35500 + 2.22589 * Asinh((Xi − 0.249797)/0.107893)

IV

−0.033

0.986

−1.020

0.953

0.477

0.997

Yi = 1.60202 + 1.27419 * Ln((Xi − 0.249246)/(2.24633 − Xi))

V

0.031

1.001

−0.971

1.032

1.009

2.610

Yi = 1.12010 + 0.815060 * Ln((Xi − 0.720331)/(4.73023 − Xi))

Back to article page