Lupine Publishers Biostatistics Biometrics Journal
Friday, 23 August 2019
Lupine Publishers: Lupine Publishers  Use of Dietary Yeast and its P...
Lupine Publishers: Lupine Publishers  Use of Dietary Yeast and its P...: Lupine Publishers  Journal of Veterinary Science Abstract All around the world, sheeps and goats play an important role in ...
Wednesday, 14 August 2019
Lupine Publishers: Eating Disorders in Developing Countries  Lupine ...
Lupine Publishers: Eating Disorders in Developing Countries  Lupine ...: Open Access Journal of Neurology  Lupine Publishers Editorial Eating disorders, once thought to be a set of rare disea...
Friday, 2 August 2019
Lupine Publishers: Lupine Publishers  Molecular Typing Of Capsular P...
Lupine Publishers: Lupine Publishers  Molecular Typing Of Capsular P...: Lupine Publishers  Journal of Veterinary Science Abstract Forty five Staphylococcus aureus isolated from cases of bovin...
Monday, 22 July 2019
The TR {Generalized Lambda V} Families of Distributions
Lupine
Publishers Biostatistics and Biometrics Open Access Journal
he fourparameter generalized lambda distribution (GLD) was proposed in [1]. We say the GLD is of type V, if the quantile function corresponds to Case(v) in of [2], that is,
where u 2 (0, 1) and a, b 2 (−1, 0). In this short note, we introduce the TR {Generalized Lambda V} Families of Distributions and show a submodel of this class of distributions is significant in modeling real life data, in particular the Wheaton river data, [2]. We conjecture the new class of distributions can be used to fit biological and health data.
Keywords and Phrases: Generalized Lambda Distribution; Exponential Distribution; Weibull Distribution
Contents
b) The New Distribution
c) Practical Significance
d) Open Problem
The T – R {Y} Family of Distributions
This family of distributions was proposed in [3]. In particular, let T, R, Y be random variables with CDF’s FT (x) = P (T _ x), FR(x) = P (R _ x), and FY (x) = P (Y _ x), respectively. Let the corresponding quantile functions be denoted by QT (p), QR(p), and QY (p), respectively. Also, if the densities exist, let the corresponding PDF’s be denoted by fT (x), fR(x), and fY (x), respectively. Following this notation, the, the CDF of the T – R {Y} is given byand the PDF of the TR{Y} family is given by
The New Distribution
Theorem: The CDF of the TR {Generalized Lambda V} Families of Distributions is given bywhere the random variable R has CDF FR(x), the random variable T with support (0,1) has CDF FT, and a, b 2 (−1, 0) Proof. Consider the integral
and let Y follow the generalized lambda class of distributions of type V, where the quantile is as stated in the abstract
Remark: the PDF can be obtained by differentiating the CDF
Practical Significance
In this section, we show a submodel of the new distribution defined in the previous section is significant in modeling real life data. We assume T is standard exponential so that FT (t) = 1 − e−t, t > 0 and R follows the twoparameter Weibull distribution, so thatNow from Theorem 2.1, we have the following
Theorem: The CDF of the Standard ExponentialWeibull {Generalized Lambda V}
Families of Distributions is given by
where c, d > 0 and a, b 2 (−1, 0)
By differentiating the CDF, we obtain the following
Theorem: the PDF of the Standard ExponentialWeibull {Generalized Lambda V} Families of Distributions is given by
where c, d > 0 and a, b 2 (−1, 0)
Remark: If a random variable B follows the Standard ExponentialWeibull {Generalized
Lambda V} Families of Distributions write
B _ SEWGLV (a, b, c, d)
Open Problem
Conjecture: The new class of distributions can be used in forecasting and modelingn of biological and health data. Related to the above conjecture is the followingQuestion: Is there a submodel of the TR {Generalized Lambda V} Families of Distributions that can fit? [3] (Appendix 1) and (Figures 13).
Appendix 1:
DataQ1 = Flatten Data11; Length DataQ1 72Min DataQ1 0.1; Max DataQ1 64.
AX1 = Empirical Distribution DataQ1
Data Distribution «Empirical», { 58}
K1 = Discrete Plot [CDF [AX1, x ], {x, 0, 65, (650)/58} , Plot Style c {Black, Thick} , Plot Markers c {Automatic, Small} , Filling c None,
Plot Range c All]
(Figure 1)
F1 x_, a_, b: = 1  1  x ^ ab
CDF Weibull Distribution c, d, x
I. Weibull. nb
D 1  E^  F1 M x, c, d, a, b, xPLK1 = Sum Log MQ DataQ1, a, b, c, di, i,1, Length DataQ1;
JK=D [PLK, a];
JK1=D [PLK, b];
JK2=D [PLK, c];
JK3=D [PLK,d];
Find Root JK, JK1, JK2, JK3, a,  0.11 ,b,  0.12 , c, 0.9 , d, 11.6
a c – 7.2577, b c – 0.395297, c c 0.776499, d c 657.998
RR = Plot 1  E^  F1 M x, 0.776499, 657. 998,  7.2577,  0.395297, x, 0, 65, Plot Style c Thick, Blue, Plot Range c All
(Figure 2)
II. Weibull. nb
CMU = Show K1, RR, Plot Range c All
(Figure 3)
Export “CMU.jpg”, CMU CMU.jpg
For
more Lupine Publishers Open
Access Journals Please visit our website: https://lupinepublishersgroup.com/
For
more Bio
statistics and Bio metrics Open Access Journal articles Please Click
Here: https://lupinepublishers.com/biostatisticsbiometricsjournal/
To
Know More About Open
Access Publishers Please Click on Lupine
Publishers
Lupine Publishers: Lupine Publishers  Advances in Robotics & Mechani...
Lupine Publishers: Lupine Publishers  Advances in Robotics & Mechani...: Journal of Robotics & Mechanical Engineering  Lupine Publishers Smart Robotics for Smart Healthcare Abstract The...
Thursday, 18 July 2019
Lupine Publishers: Surfactant Mediated Biodegradation of Aromatic Hyd...
Lupine Publishers: Surfactant Mediated Biodegradation of Aromatic Hyd...: Journal of Oceanography  Lupine Publishers Abstract Aromatic hydrocarbons (toluene and xylene) are highly water soluble and their...
Monday, 1 July 2019
Lupine Publishers: Insight Virtual Humanoid Robotics Modeling: the Ul...
Lupine Publishers: Insight Virtual Humanoid Robotics Modeling: the Ul...: Insight Virtual Humanoid Robotics Modeling: the Ultimate Level 0f Artificial Intelligence by Sadique Shaikh in ARME in Lupine Publisher...
Subscribe to:
Posts (Atom)
Lupine Publishers: Lupine Publishers  Use of Dietary Yeast and its P...
Lupine Publishers: Lupine Publishers  Use of Dietary Yeast and its P... : Lupine Publishers  Journal of Veterinary Science Abstract ...

EMuser (Enhanced Multiple Sclerosis Expected Rate): A Technical Improvement by Davide Frumento in Current Trends on Biostatistics and...

I s there any Relationship between Human Eyesight and Urine Nitrites? by Daima Hamid in Current Trends on Biostatistics & Biome...

Visualization of Voxel Volume Emission and Absorption of Light in Medical Biology by Afeez Mayowa Babalola in Current Trends on Biostat...