calculo poblacional

ANEXO I: CALCULO POBLACIONAL DISTRITO DE SANTA CRUZ DE FLORES

1 METODO ARITMETICO

1.1 DATOS HISTORICOS A NIVEL DISTRITAL:

Censo PoblaciónTotal Población urbana Población Rural

1941 1543 1035 5081961 2277 1232 10451972 2577 1485 10921981 2456 1357 10991993 2131 1466 665

2007 2547 1585 962FUENTE: INEI-Censos Nacionales: 1941,1961,1972, 1981,1993 y 2007

Ecuación : Pf = Po ( 1 + r t )

a). Combinaciones con dos censos :

Censos Tasa ( % )

1,941 1,961 === > r1 = 2.38%

1,941 1,972 === > r2 = 2.16%

1,941 1,981 === > r3 = 1.48%

1,941 1,993 === > r4 = 0.73%

1,941 2,007 === > r5 = 0.99%

1,961 1,972 === > r6 = 1.20%

1,961 1,981 === > r7 = 0.39%

1,961 1,993 === > r8 = -0.20%

1,961 2,007 === > r9 = 0.26%

1,972 1,981 === > r10 = -0.52%

1,972 1,993 === > r11 = -0.82%

1,972 2,007 === > r12 = -0.03%

1,981 1,993 === > r13 = -1.10%

1,981 2,007 === > r14 = 0.14%

1,993 2,007 === > r15 = 1.39%

b). Comportamiento histórico de las ecuaciones :

Curva Tasa 1941 1961 1972 1981 1993 2007 Sumatoria Diferencia

Censo 1,543 2,277 2,577 2,456 2,131 2,547 13,531 ---

1 2.38% 991 1,216 1,389 1,573 1,910 2,547 9,626 3,905

2 2.16% 1,049 1,277 1,449 1,630 1,955 2,547 9,907 3,624

3 1.48% 1,288 1,515 1,678 1,839 2,110 2,547 10,977 2,554

4 0.73% 1,716 1,904 2,027 2,139 2,310 2,547 12,643 888

5 0.99% 1,543 1,752 1,893 2,027 2,238 2,547 12,000 1,531

6 1.20% 1,422 1,642 1,794 1,942 2,181 2,547 11,528 2,003

7 0.39% 2,022 2,156 2,238 2,310 2,414 2,547 13,687 156

8 -0.20% 2,935 2,805 2,739 2,686 2,620 2,547 16,332 2,801

9 0.26% 2,176 2,277 2,336 2,387 2,458 2,547 14,181 650

10 -0.52% 3,884 3,351 3,115 2,946 2,747 2,547 18,590 5,059

11 -0.82% 5,584 4,102 3,579 3,241 2,879 2,547 21,932 8,401

12 -0.03% 2,604 2,586 2,577 2,569 2,558 2,547 15,441 1,910

13 -1.10% 9,357 5,169 4,147 3,570 3,012 2,547 27,802 14,271

14 0.14% 2,328 2,390 2,425 2,456 2,497 2,547 14,643 1,112

15 1.39% 1,326 1,551 1,711 1,869 2,131 2,547 11,135 2,396

Curva seleccionada: Po = 2,547 habitantes

r = 2.38 %

2 METODO GEOMETRICO



1,941 1,543 1,035 508

1,961 2,277 1,232 1,045

1,972 2,577 1,485 1,092

1,981 2,456 1,357 1,099

1,993 2,131 1,466 665

2,007 2,547 1,585 962

FUENTE: INEI-Censos Nacionales: 1941,1961,1972, 1981,1993 y 2007

Ecuación : Pf = Po ( 1 + r ) ^ t


Censos Tasa ( % )

1,941 1,961 === > r1 = 1.96%

1,941 1,972 === > r2 = 0.40%

1,941 1,981 === > r3 = -0.12%

1,941 1,993 === > r4 = -0.27%

1,941 2,007 === > r5 = 0.27%

1,961 1,972 === > r6 = 1.13%

1,961 1,981 === > r7 = -0.24%

1,961 1,993 === > r8 = -0.44%

1,961 2,007 === > r9 = 0.39%

1,972 1,981 === > r10 = -0.53%

1,972 1,993 === > r11 = -0.90%

1,972 2,007 === > r12 = -0.03%

1,981 1,993 === > r13 = -1.18%

1,981 2,007 === > r14 = 0.14%

1,993 2,007 === > r15 = 1.28%

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

METODO ARITMETICO

Censo 1 2 3 4 5 6 7 8 10 11 12 13 14 15TIEMPO (Años)

PO

BL

AC

ION

(H

ab)


Curva Tasa 1,941 1,961 1972 1981 1993 2007 Sumatoria Diferencia

Censo ----- 1,543 2,277 2,577 2,456 2,131 2,547 9,711 ---

1 1.96% 705 1,040 1,289 1,536 1,940 2,547 9,057 654.3

2 0.40% 1,957 2,119 2,214 2,296 2,409 2,547 13,541 3,830.4

3 -0.12% 2,757 2,691 2,656 2,628 2,590 2,547 15,869 6,158.1

4 -0.27% 3,049 2,887 2,802 2,734 2,646 2,547 16,666 6,954.6

5 0.27% 2,131 2,249 2,317 2,374 2,452 2,547 14,071 4,359.7

6 1.13% 1,212 1,517 1,717 1,901 2,176 2,547 11,070 1,358.8

7 -0.24% 2,985 2,844 2,770 2,711 2,634 2,547 16,492 6,780.5

8 -0.44% 3,413 3,123 2,974 2,858 2,710 2,547 17,626 7,914.5

9 0.39% 1,972 2,131 2,223 2,303 2,412 2,547 13,588 3,877.2

10 -0.53% 3,624 3,256 3,070 2,927 2,745 2,547 18,168 8,457.5

11 -0.90% 4,628 3,861 3,496 3,223 2,891 2,547 20,646 10,934.6

12 -0.03% 2,603 2,586 2,577 2,569 2,559 2,547 15,441 5,730.2

13 -1.18% 5,560 4,388 3,853 3,464 3,006 2,547 22,818 13,106.8

14 0.14% 2,322 2,388 2,425 2,456 2,498 2,547 14,636 4,924.6

15 1.28% 1,098 1,417 1,630 1,829 2,131 2,547 10,652 940.9


r = 1.96 %

3 METODO PARABOLICO:



1,941 1,543 1,035 508

1,961 2,277 1,232 1,045

1,972 2,577 1,485 1,092

1,981 2,456 1,357 1,099

1,993 2,131 1,466 665

2,007 2,547 1,585 962


Ecuación : Pf = A + B t + C t ^ 2

1,930 1,940 1,950 1,960 1,970 1,980 1,990 2,000 2,010 2,020

0

1,000

2,000

3,000

4,000

5,000

6,000

METODO GEOMETRICO

Censo 1 2 3 4 5 6 7 8 9 10 11 12 13 14

15

TIEMPO (Años)

PO

BL

AC

ION

(H

ab)

a). Combinaciones con tres censos :

t ^ 0 t t ^ 2 Pf Determinacion de Coeficientes

1 -66 4,356 1,543 Det. Coef. = 6820 Det. B = 18006

1 -46 2,116 2,277 Det. A = 20746000 Det. C = -2074

1 -35 1,225 2,577

1 -66 4,356 1,543 Det. Coef. = 16000 Det. B = -656000

1 -46 2,116 2,277 Det. A = 29743600 Det. C = -11100

1 -26 676 2,456

1 -66 4,356 1,543 Det. Coef. = 33280 Det. B = -1736320

1 -46 2,116 2,277 Det. A = 51787168 Det. C = -26408

1 -14 196 2,131

1 -66 4,356 1,543 Det. Coef. = 60720 Det. B = -948344

1 -46 2,116 2,277 Det. A = 154653840 Det. C = -28364

1 0 0 2,547

1 -46 2,116 2,277 Det. Coef. = 1980 Det. B = -272511

1 -35 1,225 2,577 Det. A = 502550 Det. C = -4031

1 -26 676 2,456

1 -46 2,116 2,277 Det. Coef. = 7392 Det. B = -706086

1 -35 1,225 2,577 Det. A = 8063524 Det. C = -11206

1 -14 196 2,131

1 -46 2,116 2,277 Det. Coef. = 17710 Det. B = -394230

1 -35 1,225 2,577 Det. A = 45107370 Det. C = -10830

1 0 0 2,547

1 -35 1,225 2,577 Det. Coef. = 2268 Det. B = -120345

1 -26 676 2,456 Det. A = 3436986 Det. C = -1473

1 -14 196 2,131

1 -35 1,225 2,577 Det. Coef. = 8190 Det. B = 131755

1 -26 676 2,456 Det. A = 20859930 Det. C = 3965

1 0 0 2,547

1 -35 1,225 2,577 Det. Coef. = 10290 Det. B = 515480

1 -14 196 2,131 Det. A = 26208630 Det. C = 14980

1 0 0 2,547

1 -26 676 2,456 Det. Coef. = 4368 Det. B = 263380

1 -14 196 2,131 Det. A = 11125296 Det. C = 9542

1 0 0 2,547

Censos Tasa ( % )

1941 1961 1972 === > A1 = 2,547.00

B1 = 2.64

C1 = -0.30

1941 1961 1981 === > A2 = 2,547.00

B2 = -41.00

C2 = -0.69

1941 1961 1993 === > A3 = 2,547.00

B3 = -52.17

C3 = -0.79

1941 1961 2007 === > A4 = 2,547.00

B4 = -15.62

C4 = -0.47

1961 1972 1981 === > A5 = 2,547.00

B5 = -137.63

C5 = -2.04

1961 1972 1993 === > A6 = 2,547.00

B6 = -95.52

C6 = -1.52

1961 1972 2007 === > A7 = 2,547.00

B7 = -22.26

C7 = -0.61

1972 1981 1993 === > A8 = 2,547.00

B8 = -53.06

C8 = -0.65

1972 1981 2007 === > A9 = 2,547.00

B9 = 16.09

C9 = 0.48

1972 1993 2007 === > A10 = 2,547.00

B10 = 50.10

C10 = 1.46

1981 1993 2007 === > A11 = 2,547.00

B11 = 60.30

C11 = 2.18

b). Mínimos cuadrados :

Mínimos cuadrados : Pf = A + B t + C t ^ 2

t Pf t Pf t ^ 2 Pf t ^ 2 t ^ 3 t ^ 4

0 2,547 0 0 0 0 0

-14 2,131 (29,834) 196 417,676 (2,744) 38,416

-26 1,357 (35,282) 676 917,332 (17,576) 456,976

-35 2,577 (90,195) 1,225 3,156,825 (42,875) 1,500,625

-46 2,277 (104,742) 2,116 4,818,132 (97,336) 4,477,456

-66 1,543 (101,838) 4,356 6,721,308 (287,496) 18,974,736

-187 12,432 (361,891) 8,569 16,031,273 (448,027) 25,448,209

Determinacion de Coeficientes

8569 (448,027) (65,496)

-448027 25,448,209 2,449,408 Det. Coef. = 1.734E+10

Det. B = -5.694E+11

Det. C = -8.355E+9

Censos Coeficientes

=== > A5 = 2,547.00

1941 1961 1972 1981 1993 2007 B5 = -32.84

C5 = -0.48

c). Comportamiento histórico de las ecuaciones :

Curva 1941 1961 1972 1981 1993 2007 Sumatoria DiferenciaCenso 1,941 1,961 2,577 2,456 2,131 2,547 9,711 ---

1 1,048 1,782 2,082 2,272 2,450 2,547 12,181 2,470

2 2,231 2,965 3,132 3,144 2,985 2,547 17,004 7,293

3 2,533 3,267 3,401 3,367 3,121 2,547 18,236 8,525

4 1,543 2,277 2,521 2,637 2,674 2,547 14,199 4,488

5 2,762 4,570 4,870 4,749 4,074 2,547 23,572 13,861

6 2,247 3,733 4,033 4,005 3,587 2,547 20,152 10,441

7 1,352 2,277 2,577 2,712 2,738 2,547 14,203 4,492

8 3,220 3,613 3,608 3,487 3,162 2,547 19,637 9,926

9 3,594 2,831 2,577 2,456 2,416 2,547 16,421 6,710

10 5,582 3,323 2,577 2,228 2,131 2,547 18,388 8,677

11 8,083 4,395 3,112 2,456 2,131 2,547 22,724 13,013

12 2,615 3,037 3,106 3,075 2,912 2,547 17,292 7,581

Curva seleccionada: A = 2,547.00

B = 50.10

C = 1.46

5 DETERMINACION DEL MODELO DE CRECIMIENTO POBLACIONAL

Cálculo de la población futura tomando como referencia el crecimiento vegetativo

de la Provincia

2.30 % En base al cuadro anterior

Año Censo Aritmético Geométrico Parabólico Curva 2.59%

Elegida

2,007 2,547 2,547 2,547 2,547 2,547

2,008 2,606 2,608 2,597 2,599 2,599

2,009 2,666 2,668 2,648 2,653 2,653

2,010 2,727 2,729 2,700 2,710 2,710

2,011 2,790 2,789 2,753 2,771 2,771

2,012 2,854 2,850 2,807 2,834 2,834

0 2,013 2,919 2,911 2,862 2,900 2,900

1 2,014 2,986 2,971 2,918 2,969 2,969

2 2,015 3,055 3,032 2,975 3,041 3,041

3 2,016 3,125 3,093 3,033 3,116 3,116

4 2,017 3,197 3,153 3,093 3,194 3,194

5 2,018 3,271 3,214 3,153 3,274 3,274

6 2,019 3,346 3,274 3,215 3,358 3,358

7 2,020 3,423 3,335 3,278 3,444 3,444

8 2,021 3,502 3,396 3,342 3,534 3,534

9 2,022 3,582 3,456 3,408 3,626 3,626

10 2,023 3,665 3,517 3,475 3,721 3,721

11 2,024 3,749 3,578 3,543 3,819 3,819

12 2,025 3,835 3,638 3,612 3,920 3,920

13 2,026 3,923 3,699 3,683 4,024 4,024

14 2,027 4,014 3,759 3,755 4,131 4,131

15 2,028 4,106 3,820 3,829 4,241 4,241

16 2,029 4,200 3,881 3,904 4,354 4,354

17 2,030 4,297 3,941 3,980 4,469 4,469

18 2,031 4,396 4,002 4,058 4,588 4,588

Tasa de crecimento referencial provincial

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020

500

1,500

2,500

3,500

4,500

5,500

6,500

7,500

8,500

METODO PARABOLICO

Censo 1 2 3 4 5 6 7 8 9 10 11 12

TIEMPO (Años)

PO

BL

AC

ION

(H

ab)

19 2,032 4,497 4,062 4,138 4,709 4,709

20 2,033 4,600 4,123 4,219 4,834 4,834

21 2,034 4,706 4,184 4,302 4,961 4,961

22 2,035 4,814 4,244 4,386 5,091 5,091

Sumatoria 103,399 98,474 98,210 105,432 105,432

Diferencia - (4,925) (5,189) 2,032

2,005 2,010 2,015 2,020 2,025 2,030 2,035 2,040

0

1,000

2,000

3,000

4,000

5,000

6,000

CURVA DE CRECIMIENTO POBLACIONAL

Censo Aritmético Geométrico Parabólico

TIEMPO (Años)

PO

BL

AC

ION

(H

ab)

ANEXO I: CALCULO POBLACIONAL DE LA PROVINCIA DE CAÑETE

1 METODO ARITMETICO



1941 47156 18907 282491961 72226 30311 419151972 90559 47218 433411981 113126 79887 332391993 152378 111447 40931

2007 200662 168584 32078FUENTE: INEI-Censos Nacionales: 1941,1961,1972, 1981,1993 y 2007

Ecuación : Pf = Po ( 1 + r t )


Censos Tasa ( % )

1,941 1,961 === > r1 = 2.66%

1,941 1,972 === > r2 = 2.97%

1,941 1,981 === > r3 = 3.50%

1,941 1,993 === > r4 = 4.29%

1,941 2,007 === > r5 = 4.93%

1,961 1,972 === > r6 = 2.31%

1,961 1,981 === > r7 = 2.83%

1,961 1,993 === > r8 = 3.47%

1,961 2,007 === > r9 = 3.87%

1,972 1,981 === > r10 = 2.77%

1,972 1,993 === > r11 = 3.25%

1,972 2,007 === > r12 = 3.47%

1,981 1,993 === > r13 = 2.89%

1,981 2,007 === > r14 = 2.98%

1,993 2,007 === > r15 = 2.26%


Curva Tasa 1941 1961 1972 1981 1993 2007 Sumatoria Diferencia

Censo 47,156 72,226 90,559 113,126 152,378 200,662 676,107 ---

1 2.66% 72,851 90,275 103,950 118,655 146,239 200,662 732,632 56,525

2 2.97% 67,800 84,818 98,403 113,243 141,743 200,662 706,669 30,562

3 3.50% 60,653 76,916 90,221 105,095 134,704 200,662 668,251 7,856

4 4.29% 52,363 67,474 80,204 94,845 125,354 200,662 620,902 55,205

5 4.93% 47,156 61,386 73,602 87,917 118,698 200,662 589,421 86,686

6 2.31% 79,534 97,339 111,008 125,417 151,665 200,662 765,625 89,518

7 2.83% 69,948 87,151 100,785 115,577 143,700 200,662 717,823 41,716

8 3.47% 61,013 77,318 90,642 105,519 135,079 200,662 670,233 5,874

9 3.87% 56,502 72,226 85,278 100,075 130,197 200,662 644,940 31,167

10 2.77% 70,969 88,254 101,905 116,670 144,606 200,662 723,066 46,959

11 3.25% 63,794 80,415 93,866 108,749 137,903 200,662 685,389 9,282

12 3.47% 60,941 77,239 90,559 105,435 135,005 200,662 669,841 6,266

13 2.89% 68,994 86,118 99,731 114,547 142,839 200,662 712,891 36,784

14 2.98% 67,694 84,702 98,284 113,126 141,644 200,662 706,112 30,005

15 2.26% 80,463 98,308 111,965 126,323 152,378 200,662 770,099 93,992


r = 3.87 %

2 METODO GEOMETRICO



1,941 47,156 18,907 28,249

1,961 72,226 30,311 41,915

1,972 90,559 47,218 43,341

1,981 113,126 79,887 33,239

1,993 152,378 111,447 40,931

2,007 200,662 168,584 32,078


Ecuación : Pf = Po ( 1 + r ) ^ t


Censos Tasa ( % )

1,941 1,961 === > r1 = 2.15%

1,941 1,972 === > r2 = 0.73%

1,941 1,981 === > r3 = 0.56%

1,941 1,993 === > r4 = 0.57%

1,941 2,007 === > r5 = 0.42%

1,961 1,972 === > r6 = 2.08%

1,961 1,981 === > r7 = 1.12%

1,961 1,993 === > r8 = 0.94%

1,961 2,007 === > r9 = 0.60%

1,972 1,981 === > r10 = 2.50%

1,972 1,993 === > r11 = 2.51%

1,972 2,007 === > r12 = 2.30%

1,981 1,993 === > r13 = 2.51%

1,981 2,007 === > r14 = 2.23%

1,993 2,007 === > r15 = 1.99%

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020

0

50,000

100,000

150,000

200,000

250,000

METODO ARITMETICO

Censo 1 2 3 4 5 6 7 8 10 11 12 13 14 15TIEMPO (Años)

PO

BL

AC

ION

(H

ab)


Curva Tasa 1,941 1,961 1972 1981 1993 2007 Sumatoria Diferencia

Censo ----- 47,156 72,226 90,559 113,126 152,378 200,662 556,725 ---

1 2.15% 49,141 75,267 95,157 115,282 148,887 200,662 684,396 127,671.1

2 0.73% 123,969 143,447 155,435 165,986 181,176 200,662 970,675 413,949.7

3 0.56% 139,003 155,360 165,163 173,642 185,628 200,662 1,019,459 462,733.5

4 0.57% 137,492 154,181 164,208 172,896 185,199 200,662 1,014,638 457,912.6

5 0.42% 152,377 165,633 173,408 180,041 189,281 200,662 1,061,403 504,677.7

6 2.08% 51,646 77,920 97,698 117,562 150,465 200,662 695,953 139,227.6

7 1.12% 96,290 120,285 135,944 150,261 171,721 200,662 875,163 318,437.6

8 0.94% 108,557 130,770 144,869 157,529 176,145 200,662 918,532 361,806.9

9 0.60% 135,190 152,378 162,745 171,750 184,537 200,662 1,007,262 450,536.9

10 2.50% 39,249 64,353 84,465 105,514 141,955 200,662 636,198 79,472.8

11 2.51% 39,102 64,185 84,297 105,358 141,842 200,662 635,446 78,720.9

12 2.30% 44,759 70,523 90,559 111,118 145,966 200,662 663,587 106,861.7

13 2.51% 38,992 64,059 84,171 105,241 141,757 200,662 634,882 78,157.4

14 2.23% 46,841 72,794 92,769 113,126 147,381 200,662 673,573 116,847.7

15 1.99% 54,815 81,223 100,834 120,353 152,378 200,662 710,265 153,540.0


r = 2.30 %

1,930 1,940 1,950 1,960 1,970 1,980 1,990 2,000 2,010 2,020

0

50,000

100,000

150,000

200,000

250,000

METODO GEOMETRICO

Censo 1 2 3 4 5 6 7 8 9 10 11 12 13 14

15

TIEMPO (Años)

PO

BL

AC

ION

(H

ab)

5 DETERMINACION DEL MODELO DE CRECIMIENTO POBLACIONAL

Cálculo de la población futura tomando como referencia el crecimiento provincial

Tasa de crecimento referencial 2.30 % En base al cuadro anterior

Año Censo Aritmético Geométrico 2.30%

2,007 200,662 200,662 200,662

2,008 205,277 208,428 205,277

2,009 209,999 216,193 209,999

2,010 214,829 223,959 214,829

2,011 219,770 231,724 219,770

BASE 2,012 224,824 239,490 224,824

0 2,013 229,995 247,256 229,995

1 2,014 235,285 255,021 235,285

2 2,015 240,697 262,787 240,697

3 2,016 246,233 270,553 246,233

4 2,017 251,896 278,318 251,896

5 2,018 257,690 286,084 257,690

6 2,019 263,617 293,849 263,617

7 2,020 269,680 301,615 269,680

8 2,021 275,882 309,381 275,882

9 2,022 282,228 317,146 282,228

10 2,023 288,719 324,912 288,719

11 2,024 295,359 332,678 295,359

12 2,025 302,153 340,443 302,153

13 2,026 309,102 348,209 309,102

14 2,027 316,212 355,974 316,212

15 2,028 323,484 363,740 323,484

16 2,029 330,925 371,506 330,925

17 2,030 338,536 379,271 338,536

18 2,031 346,322 387,037 346,322

19 2,032 354,288 394,802 354,288

20 2,033 362,436 402,568 362,436

21 2,034 370,772 410,334 370,772

22 2,035 379,300 418,099 379,300

Sumatoria 8,146,171 8,972,039 8,146,171

Diferencia - 825,868 0

2,005 2,010 2,015 2,020 2,025 2,030 2,035 2,040

180,000

230,000

280,000

330,000

380,000

430,000

480,000

CURVA DE CRECIMIENTO POBLACIONAL

Censo Aritmético Geométrico

TIEMPO (Años)

PO

BL

AC

ION

(H

ab)

calculo poblacional

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