मैं एक गामा वितरण के मापदंडों का अनुमान लगाने की कोशिश कर रहा हूं जो मेरे डेटा नमूने के लिए सबसे उपयुक्त हैं। मैं केवल डेटा नमूने से माध्य , एसटीडी (और इसलिए विचरण ) का उपयोग करना चाहता हूं , वास्तविक मूल्यों का नहीं - क्योंकि ये हमेशा मेरे आवेदन में उपलब्ध नहीं होंगे।
के अनुसार इस दस्तावेज़, निम्नलिखित फार्मूले आकार और पैमाने अनुमान लगाने के लिए लागू किया जा सकता:
मैंने अपने डेटा के लिए यह कोशिश की, हालांकि एक पायथन प्रोग्रामिंग लाइब्रेरी का उपयोग करके वास्तविक डेटा पर एक गामा वितरण को फिट करने की तुलना में परिणाम बहुत अलग हैं।
मैं हाथ में समस्या दिखाने के लिए अपना डेटा / कोड संलग्न करता हूं:
import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import gamma
data = [91.81, 10.02, 27.61, 50.48, 3.34, 26.35, 21.0, 79.27, 31.04, 8.85, 109.2, 15.52, 11.03, 41.09, 10.75, 96.43, 109.52, 33.28, 7.66, 65.44, 52.43, 19.25, 10.97, 586.52, 56.91, 157.18, 434.74, 16.07, 334.43, 6.63, 108.41, 4.45, 42.03, 39.75, 300.17, 4.37, 343.19, 32.04, 42.57, 29.53, 276.75, 15.43, 117.67, 75.47, 292.43, 457.91, 5.49, 17.69, 10.31, 58.91, 76.94, 37.39, 64.46, 187.25, 30.0, 9.94, 83.05, 51.11, 17.68, 81.98, 4.41, 33.24, 20.36, 8.8, 846.0, 154.24, 311.09, 120.72, 65.13, 25.52, 50.9, 14.27, 17.74, 529.82, 35.13, 124.68, 13.21, 88.24, 12.12, 254.32, 22.09, 61.7, 88.08, 18.75, 14.34, 931.67, 19.98, 50.86, 7.71, 5.57, 8.81, 14.49, 26.74, 13.21, 8.92, 26.65, 10.09, 7.74, 21.23, 66.35, 31.81, 36.61, 92.29, 26.18, 20.55, 17.18, 35.44, 6.63, 69.0, 8.81, 19.87, 5.46, 29.81, 122.01, 57.83, 33.04, 9.91, 196.0, 34.26, 34.31, 36.55, 7.74, 6.68, 6.83, 18.83, 6.6, 50.78, 95.65, 53.91, 81.62, 57.96, 26.72, 76.25, 5.48, 4.43, 133.04, 33.37, 45.26, 30.51, 9.98, 11.08, 28.95, 71.25, 70.65, 3.34, 12.28, 111.67, 139.86, 23.34, 30.0, 26.38, 33.51, 1112.64, 25.87, 148.59, 552.79, 11.11, 47.8, 7.8, 9.98, 7.69, 85.46, 3.59, 122.71, 32.09, 82.51, 12.14, 12.57, 8.8, 49.61, 95.41, 26.99, 13.29, 4.57, 7.78, 4.4, 6.66, 12.17, 12.18, 1533.01, 22.95, 15.93, 14.82, 2.2, 12.04, 9.94, 17.64, 6.66, 18.64, 83.66, 142.99, 30.76, 67.57, 9.88, 46.44, 19.5, 22.2, 43.1, 653.67, 9.86, 7.69, 7.74, 27.19, 38.64, 12.32, 182.34, 43.13, 3.28, 14.32, 69.78, 32.2, 17.66, 18.67, 4.4, 9.05, 56.94, 33.32, 13.2, 15.07, 12.73, 3.32, 35.44, 14.35, 66.68, 51.28, 6.86, 75.49, 5.54, 21.0, 24.2, 38.1, 13.31, 7.78, 5.76, 51.86, 11.09, 20.71, 36.74, 21.97, 10.36, 32.04, 96.94, 13.93, 51.84, 6.88, 27.58, 100.56, 20.97, 828.16, 6.63, 32.15, 19.92, 253.23, 25.35, 23.35, 17.6, 43.18, 19.36, 13.7, 3.31, 22.99, 26.58, 4.43, 2.22, 55.46, 22.34, 13.24, 86.18, 181.29, 52.15, 5.52, 21.12, 34.24, 49.78, 14.37, 39.73, 78.22, 26.6, 20.19, 26.57, 105.8, 11.08, 46.47, 52.82, 13.46, 8.0, 7.74, 49.73, 4.4, 5.44, 51.7, 28.64, 8.95, 9.15, 4.46, 21.03, 29.92, 19.89, 4.38, 19.94, 7.77, 23.43, 57.07, 86.5, 12.82, 103.85, 39.63, 8.83, 42.32, 17.02, 14.29, 16.75, 24.4, 27.97, 8.83, 8.91, 24.23, 6.58, 30.97, 150.58, 122.73, 17.69, 37.11, 11.05, 298.23, 25.58, 9.91, 38.85, 17.24, 82.17, 42.11, 3.29, 38.63, 27.55, 18.22, 127.16, 57.66, 34.45, 41.26, 45.91, 9.88, 34.48, 484.33, 58.42, 30.09, 6.69, 254.49, 1313.58, 39.89, 3.31, 7.83, 10.98, 13.21, 67.78, 7.77, 117.72, 20.03, 83.23, 31.28, 38.97, 6.63, 6.63, 36.6, 22.12, 154.57, 112.65, 19.88, 674.18, 83.31, 5.54, 8.81, 11.06, 178.33, 30.47, 1180.39, 79.33, 37.74, 86.3, 16.61, 53.94, 52.78, 20.83, 11.15, 26.68, 86.04, 180.26, 99.62, 11.17, 28.74, 56.85, 15.51, 95.37, 44.09, 6.68, 12.14, 6.72, 19.81, 10.05, 34.26, 69.84, 14.35, 17.72, 8.81, 20.86, 37.69, 24.62, 72.11, 8.83, 7.69, 60.79, 20.02, 9.41, 13.24, 29.8, 43.09, 25.34, 174.34, 161.6, 119.34, 30.08, 54.15, 7.74, 249.29, 9.98, 21.87, 38.92, 98.45, 95.07, 7.74, 4.45, 81.98, 12.18, 28.66, 5.58, 59.94, 22.15, 9.98, 18.86, 6.69, 134.97, 13.29, 4.43, 8.88, 5.74, 25.16, 122.39, 3.53, 6.68, 3.4, 17.58, 62.51, 584.3, 46.63, 21.19, 22.14, 5.74, 8.19, 7.74, 7.64, 4.41, 3.32, 130.76, 3.29, 31.04, 3.26, 18.83, 168.31, 7.68, 120.19, 43.95, 747.12, 18.75, 306.24, 29.72, 5.57, 6.65, 53.2, 7.96, 25.34, 25.57, 8.85, 93.59, 92.96, 23.4, 60.0, 6.63, 12.15, 49.98, 39.75, 7.77, 5.73, 18.74, 11.58, 281.32, 13.99, 4.59, 13.35, 25.05, 9.98, 5.58, 91.43, 288.94, 15.43, 7.8, 9.92, 18.69, 6.63, 78.38, 18.86, 63.03, 26.38, 166.41, 27.78, 54.21, 173.32, 11.12, 17.85, 14.43, 31.31, 3.37, 16.63, 5.51, 77.74, 8.89, 17.71, 3.24, 9.28, 22.12, 2.2, 19.41, 12.23, 22.31, 9.36, 18.85, 51.5, 8.3, 23.0, 29.7, 29.81, 4.65, 75.77, 55.52, 144.45, 6.68, 13.26, 72.78, 56.71, 46.35, 6.63, 8.88, 6.61, 41.7, 15.09, 5.51, 18.78, 74.09, 487.0, 27.52, 18.99, 44.18, 41.76, 6.65, 23.62, 175.68, 446.38, 87.13, 165.69, 16.57, 7.88, 16.57, 80.17, 135.75, 3.29, 134.16, 25.58, 45.13, 114.23, 471.15, 97.75, 12.2, 32.01, 62.21, 22.36, 193.55, 210.65, 42.39, 27.57, 106.15, 44.76, 16.6, 134.76, 18.81, 14.76, 7.97, 160.59, 39.21, 60.36, 62.45, 72.18, 91.15, 23.71, 105.04, 70.87, 25.57, 122.09, 60.09, 38.8, 133.87, 4.41, 13.28, 45.63, 45.41, 67.81, 26.68, 97.33, 723.5, 5.51, 164.05, 165.32, 4.45, 57.67, 85.82, 11.56, 12.26, 17.97, 31.04, 76.72, 15.01, 35.88, 32.37, 23.63, 85.57, 9.34, 4.45, 90.25, 73.71, 45.99, 14.24, 176.85, 65.21, 9.92, 15.02, 12.9, 21.4, 59.94, 64.62, 37.53, 147.89, 36.52, 97.67, 16.65, 22.1, 23.38, 76.85, 16.58, 7.72, 17.75, 91.25, 9.91, 18.46, 4.45, 3.29, 73.18, 19.5, 5.58, 18.85, 28.64, 7.8, 43.74, 4.43, 7.99, 132.4, 41.48, 14.45, 8.78, 8.14, 9.95, 2.46, 16.61, 32.71, 17.74, 4.46, 68.25, 34.55, 9.92, 181.31, 37.63, 125.22, 25.37, 24.45, 220.92, 11.09, 35.46, 588.56, 58.21, 22.39, 78.55, 135.13, 280.65, 273.41, 381.07, 60.56, 68.63, 40.17, 27.68, 23.68, 23.15, 28.8, 20.94, 21.92, 159.06, 9.94, 127.52, 32.4, 15.93, 99.09, 48.31, 104.66, 257.4, 117.08, 180.32, 66.55, 95.99, 17.74, 30.14, 270.54, 39.8, 54.77, 16.04, 76.99, 5.43, 8.78, 76.96, 10.39, 18.47, 290.11, 48.35, 289.06, 10.44, 57.75, 47.83, 101.62, 96.3, 71.62, 256.97, 149.45, 22.17, 23.15, 89.25, 36.46, 90.03, 69.14, 28.27, 28.72, 17.44, 43.38, 56.72, 84.96, 25.4, 55.06, 47.68, 92.11, 6.65, 30.94, 15.38, 27.44, 516.55, 5.83, 19.45, 41.53, 110.69, 6.82, 54.09, 13.31, 89.8, 25.57, 110.89, 3.32, 93.76, 33.81, 80.87, 30.9, 58.53, 185.22, 4.38, 58.75, 189.53, 7.19, 7.8, 48.97, 28.8, 48.52, 45.96, 309.44, 29.16, 2.22, 255.91, 78.7, 102.67, 33.32, 43.2, 19.5, 91.59, 139.89, 5.51, 213.96, 10.02, 10.03, 39.87, 8.95, 27.74, 7.78, 65.93, 45.41, 263.21, 33.06, 5.54, 59.77, 2.2, 9.95, 14.38, 44.76, 96.45, 15.91, 133.07, 38.03, 36.43, 7.83, 105.41, 20.5, 25.35, 20.55, 119.59, 24.31, 28.81, 101.0, 67.0, 143.85, 20.55, 83.45, 60.62, 25.19, 6.65, 1745.95, 41.62, 44.96, 65.42, 9.92, 24.23, 73.56, 34.35, 75.72, 18.77, 88.59, 312.55, 56.43, 106.61, 11.44, 22.04, 5.73, 197.92, 25.32, 144.83, 145.36, 4.43, 18.33, 48.72, 33.42, 8.83, 18.85, 32.25, 88.56, 14.95, 147.39, 9.25, 35.24, 141.51, 14.41, 5.49, 42.28, 75.69, 16.96, 6.71, 17.33, 710.34, 68.92, 28.39, 24.98, 33.03, 31.06, 46.24, 36.77, 43.74, 11.48, 22.14, 13.21, 15.8, 21.9, 5.51, 20.66, 22.04, 127.0, 21.03, 36.75, 61.45, 42.12, 238.3, 57.43, 28.61, 31.31, 15.43, 8.88, 54.26, 34.01, 5.79, 8.02, 25.68, 19.67, 29.19, 4.38, 15.05, 5.57, 32.31, 81.68, 29.92, 397.98, 119.2, 5.52, 25.54, 12.78, 17.78, 100.97, 253.58, 8.92, 22.04, 22.03, 86.57, 97.27, 106.29, 33.31, 13.34, 35.57, 40.75, 6.57, 23.32, 6.63, 30.09, 62.39, 35.62, 25.23, 5.49, 77.67, 4.41, 8.77, 12.09, 32.0, 7.75, 25.44, 27.57, 25.51, 81.59, 8.83, 64.15, 48.92, 52.25, 2.2, 13.29, 15.52, 320.64, 22.26, 21.03, 79.27, 6.61, 59.38, 40.19, 43.07, 2.26, 20.97, 8.8, 205.43, 51.82, 8.78, 90.72, 6.63, 14.46, 85.62, 72.53, 29.24, 68.81, 67.6, 1.15, 13.15, 17.71, 20.06, 77.42, 167.72, 5.54, 34.45, 5.51, 54.04, 7.8, 79.91, 4.62, 66.39, 164.13, 78.1, 49.72, 19.92, 28.92, 709.25, 18.19, 875.38, 60.92, 5.55, 71.14, 301.2, 27.74, 34.26, 108.78, 88.28, 75.83, 7.82, 8.78, 44.68, 20.98, 41.9, 8.88, 124.18, 198.8, 180.0, 71.61, 119.27, 59.33, 3.28, 43.88, 14.46, 64.34, 158.59, 41.98, 32.28, 14.43, 48.49, 2.36, 14.38, 25.52, 7.83, 2.2, 292.18, 8.97, 36.18, 7.8, 8.89, 43.26, 25.35, 12.29, 6.88, 34.48, 11.09, 16.57, 35.99, 13.45, 6.6, 162.65, 13.23, 26.91, 55.62, 61.4, 48.47, 89.62, 7.77, 6.65, 11.56, 23.28, 6.66, 7.74, 4.62, 5.8, 24.56, 10.16, 8.91, 14.45, 25.37, 6.61, 75.29, 11.03, 36.75, 38.61, 36.52, 17.75, 61.87, 31.92, 120.9, 144.82, 70.98, 19.98, 80.09, 30.17, 35.48, 2.4, 42.15, 24.29, 111.26, 71.9, 158.23, 49.75, 7.75, 13.28, 10.97, 5.51, 34.37, 56.61, 138.83, 231.4, 20.17, 29.89, 20.27, 7.69, 77.35, 12.26, 1144.41, 9.95, 7.72, 196.64, 499.4, 114.38, 24.43, 94.88, 75.15, 4.48, 8.89, 196.05, 95.15, 99.28, 42.36, 234.32, 4.59, 80.97, 237.69, 89.34, 4.51, 6.68, 148.42, 108.58, 5.48, 132.38, 7.94, 204.74, 11.08, 74.24, 146.22, 79.5, 17.68, 10.51, 550.77, 45.35, 23.28, 47.57, 40.56, 114.76, 29.81, 15.51, 11.0, 26.61, 6.74, 142.82, 12.17]
डेटा के बारे में कुछ जानकारी:
मीन: 68.71313036020582, भिन्न: 19112.931263699986, मानक विचलन: 138.24952536518882, प्रशिक्षण डेटा में राशि तत्व: 1166
डेटा का हिस्टोग्राम:
फिटिंग के लिए अजगर पुस्तकालय का उपयोग करना:
x = np.linspace(0,300,1000)
# Gamma
shape, loc, scale = gamma.fit(data, floc=0)
print(shape, loc, scale)
y = gamma.pdf(x, shape, loc, scale)
plt.title('Fitted Gamma')
plt.plot(x, y)
plt.show()
पैरामीटर: 0.7369587045435088 0 93.2387797804
यह खुद अनुमान लगाया:
def calculateGammaParams(data):
mean = np.mean(data)
std = np.std(data)
shape = (mean/std)**2
scale = (std**2)/mean
return (shape, 0, scale)
eshape, eloc, escale = calculateGammaParams(data)
print(eshape, eloc, escale)
ey = gamma.pdf(x, eshape, eloc, escale)
plt.title('Estimated Gamma')
plt.plot(x, ey)
plt.show()
पैरामीटर: 0.247031406055 0 278.155443705
एक स्पष्ट रूप से बहुत बड़ा अंतर देख सकता है।
कृपया बताएं कि आपने "1 से बहुत दूर" क्या गणना की है - यह संबंधित नहीं होगा कि पल-आधारित अनुमान स्वयं अच्छे हैं या नहीं। यदि संभव हो तो अपना डेटा दें (उदाहरण के लिए यदि नमूना आकार आपके पोस्ट में शामिल करने के लिए पर्याप्त छोटा है) और आपके पैरामीटर का अनुमान है कि दोनों तरीके से गणना की गई है।
—
Glen_b -Reinstate मोनिका
मैंने अपना प्रश्न डेटा, नमूना कोड और भूखंडों के साथ अद्यतन किया है। मुझे आशा है कि इससे मेरे प्रश्न को स्पष्ट करने में मदद मिलेगी।
—
डीजेन्सेंस
आपको लगता है कि आप एक गामा वितरण फिट करना चाहते हैं नहीं लगता है। यह अधिक मौलिक प्रश्न उठाता है: आप पहली बार इस अभ्यास से क्यों गुजर रहे हैं? क्या आप किसी भी वितरण को डेटा में फिट करके पूरा करने की उम्मीद कर रहे हैं ?
—
whuber
@ जब मैं भविष्य के डेटा के बारे में कुछ धारणाएं बनाने में सक्षम होने के लिए डेटा की फिटिंग कर रहा हूं - तो बाहरी व्यवहार की पहचान करने के लिए अधिक सटीक रूप से। मैंने सुना है गामा / लॉगऑर्म इस प्रकार के डेटा के लिए एक अच्छा फिट होगा।
—
डीजेन्सेंस