> Parameters:
-" q: lower and upper tail probability
-" x: quantiles
-" loc: [optional] location parameter. Default = 0
-" scale: [optional] scale parameter. Default = 1
-" size: [tuple of ints, optional] shape or random variates.
-" moments: [optional] composed of letters [’mvsk’]; ’m’ = mean, ’v’ = variance, ’s’ = Fisher’s skew and ’k’ = Fisher’s kurtosis. (default = ’mv’).Results: Gompertz (or truncated Gumbel) continuous random variable
Code # 1 : Generating a continuous Gompertz (or truncated Gumbel) random variable
from
scipy.stats
import
gompertz
numargs
=
gompertz.numargs
[a]
=
[
0.7
,]
*
numargs
rv
=
gompertz (a)
(
" RV: "
, rv)
Output:
RV: "scipy.stats._distn_infrastructure.rv_frozen object at 0x000001E39A3E2470"Code # 2: Gompertz (or Truncated Gumbel) Random Variations and Probability Distribution
import
numpy as np
quantile
=
np.arange (
0.01
,
1
,
0.1
)
# Random Variants
R
=
gompertz.rvs (a, scale
=
2
, size
=
10
)
(
"Random Variates:"
, R)
R
=
gompertz.pdf (a, quantile, loc
=
0
, scale
=
1
)
(
"Probability Distribution:"
, R)
Output:
Random Variates: [1.29938059 1.47547887 1.33324567 1.79424061 0.45304378 1.46222247 1.29260365 0.59989705 3.58467676 1.81226267] Probability Distribution: [0.01993441 0.19813875 0.34179784 0.45591617 0.54485437 0.61240 685 0.66187043 0.69610503 0.71758726 0.72845776]Code # 3: Graphic representation.
import
numpy as np
import
matplotlib.pyplot as plt
distribution
=
np.linspace (
0
, np.minimum (rv.dist .b,
3
))
(
"Distribution:"
, distribution)
plot
=
plt.plot (distr ibution, rv.pdf (distribution))
Output:
Distribution: [0. 0.06122449 0.12244898 0.18367347 0.24489796 0.30612245 0.36734694 0.42857143 0.48979592 0.55102041 0.6122449 0.67346939 0.73469388 0.79591837 0.85714286 0.91836735 0.97959184 1.04081633 1.10204082 1.16326531 1.2244898 1.28571429 1.34693878 1.40816327 1.46938776 1.53061224 1.59183673 1.65306122 1.71428571 1.7755102 1.83673469 1.89795918 1.95918367 2.02040816 2.08163265 2.14285714 2.20408163 2.26530612 2.32653061 2.3877551 2.44897959 2.51020408 2.57142857 2.63265306 2.69387755 2.75510204 2.81632653 2.87755102 2.93877551 3. ]
![]()
Code # 4: Various Positional Arguments
import
matplotlib. pyplot as plt
import
numpy as np
x
=
np.linspace (
0
,
5
,
100
)
# Various positional arguments
y1
=
gompertz.pdf (x,
1
,
3
)
y2
=
gompertz.pdf (x ,
1
,
4
)
plt.plot (x, y1,
"*"
, x, y2,
"r--"
)
Output:
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